Principles  of  Mechanics  as  Ap. 
plied  to  the  Solar  Systeri  ,  .  . 

By 
Robert  P.  Traxler 


UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


GIFT  OF 

Pacific  Electric   Co. 


\ 


\ 


,  A?./3 
THE 

PRINCIPLES  OF  MECHANICS 

AS   APPLIED   TO 

THE    SOLAR   SYSTEM 


ILLUSTRATIONS,    SHOWING     BY    RADIATING     LINES     THE 
MANNER  IN  WHICH  THE  FORCES  OF   THE   SUN  ARE 
APPLIED   TO   THE    PLANETS,   AND   THE    MAN- 
NER  IN   WHICH    THE    FORCES    OF    THE 
SUN  AND  PLANETS  EMANATE 
FROM    THEMSELVES. 


THE  CAUSES  OF  MAGNETIC  CURRENTS,  HEAT,  OCEAN 
CURRENTS,  EARTHQUAKES,  ETC. 

AND      THE 

PRINCIPLE  OR  CAUSE  OF  THE  TIDAL  ACTION 
ILLUSTRATED. 


SAN   FRANCISCO: 
C.  A.  MUKDOCK  &  Co.,  PRINTERS. 

1889. 


BY   K.  P.    TRAXLKH. 


PREFACE. 


As  the  science  of  Astronomy  has,  from  time  almost  im- 
memorial to  the  present,  been  compelled  to  carry  with  it 
theories  which  have  been  and  are  now  more  or  less  specula- 
tive in  their  nature  and  character,  the  author  hopes,  in 
placing  this  little  work  before  the  reader,  that  it  will  not  be 
felt  as  an  additional  burden,  but  will  be  kindly  accepted 
and  considered,  and  that  the  theories  that  it  contains  will 
be  carefully  compared  with  all  applicable  natural  phenomena 
and  principles,  in  mechanics,  with  which  the  reader  may 
be  familiar  and  that  the  claims  that  are  herein  advocated 
may  be  sustained  only  by  the  merits  which  they  possess. 

Most  of  the  illustrations  which  are  used  as  explanatory  of 
the  substance  matter  contained  herein  are  necessarily  exag- 
gerated in  regard  to  sizes  and  distances,  etc.,  the  same  as 
nearly  all  astronomical  illustrations,  and  they  are  used 
mainly  to  show  the  application  of  the  theory  or  principle 
involved. 

The  author  is  well  aware  that  the  apparent  movements 
^   of  the  satellites  of  the  two  farthest    planets,  also  those  of 
^    some  of  the  comets  may  be  referred  to  as  exceptions,  but  as 
^    there  are  evidences  of  forces  in  operation  at  those  remote 
i*f    distances,  the  same  as  between  those  bodies  and  the  Sun,  it 
is  the  opinion  of  the  author  that  it  is  only  necessary  to  wait 
*ior  greater  scientific  advantages,  which  will  enable  us  to 
investigate  further  and  more  carefully,  when  natural  forces 
will   be   found    to  be  operating   upon  them  in  a  strictly 
mechanical  way. 

314018 


4  PREFACE. 

The  diameters,  distances,  times  of  revolution,  etc.,  used 
by  the  author  are  from  the  more  recent  calculations. 

It  has  been  the  effort  of  the  author  to  describe  and  illus- 
trate the  claims  herein  set  forth  by  principles  that  the 
general  reader  can  readily  understand  and  with  which  the 
common  experiences  of  life  familiarize  us.  The  use  of 
technical  terms  has  been  carefully  avoided,  as  much  as 
possible,  so  that  the  reader,  casual  or  otherwise,  may  be 
better  able  to  reject  or  approve  of  the  idea  presented  to  the 
mind  for  consideration. 

It  has  likewise  been  the  aim  of  the  author  to  reject  the 
many  opportunities  to  incite  the  mind  of  the  reader  to 
wonder,  astonishment  or  admiration,  preferring  rather  to 
represent  as  nearly  as  possible  the  operations  of  our  plane- 
tary S3rstem  within  a  space  that  will  enable  the  mind  to 
comprehend  the  movements  of  the  planets  and  comets 
revolving  around  the  Sun,  making  the  solar  system  appear 
as  a  simple  and  natural  combined  piece  of  mechanism,  or  a 
mere  toy  of  the  universe. 

Finally,  in  committing  to  the  reader  the  few  thoughts 
which  are  contained  in  this  little  work,  it  is  the  belief  of 
the  author  that  the  more  the  divine  laws,  in  all  things,  are 
studied  and  the  better  they  are  understood,  the  more  mu- 
nificent will  they  appear. 


CONTENTS. 

PAGE. 

ASTEROIDS         "'------38 

AXIAL  INCLINATIONS    ----._  27 

COMETS      ------...  47 

DISTANCES,  DIAMETERS,  ETC.,  TABLE  OF  47 

EARTH 26 

EARTHQUAKES       -                                            .        _  Q% 

HEAT                                   g4 

JUPITER                           ----__  39 

MOONS  OF     ----.__  41 

MARS  36 

MEAN  DISTANCES                46 

MERCURY      -----.._  20 
MOON         "~~"-----28 

MOONS  OF  URANUS  AND  NEPTUNE            ...  45 

NEPTUNE 45 

PLANETARY  FORMATION 69 

PLANETARY  MOTION,  THEORIES  OF     -  9 

SATURN          -----...  42 

"        MOONS  OF     -------  42 

"        RINGS  OF  43 

SUN  n 

"     FORCE  OF g 

"     MOTIONS  OF 18 

TIDES 52 

URANUS     -----....  44 

VENUS 23 


I  L  L  U  B  T  R  A  T  I  0  X  S  . 


PAGE. 

COMPARATIVE  SIZE  OF  THE  Sc;x  WITH  JUPITER  AND 

THE  EARTH        -  8 

SECTIONAL  Sft>E  AND  EDGE   VIEW  OF  THE  SUN,  ETC.  1C 

DIAGRAM   SHOWING  THE  INCLINATION  OF  THE  SUN'S 

Axis        -  18 

SECTIONAL  SIDE  VIEW  OF  THE  SOLAR  SYSTEM  21 

MOON'S   PATH    ALONG   THE  EARTH'S   ORBIT   DURING 

THE  YEARS  1888  AND  1889     •  30 

POSITION  OF  THE  TIDES  IN  RELATION  TO  THE  MOON 

AND  SUN     -                                   -        -        -        -,  57 

A  WHEEL  REPRESENTING  THE  EARTH  58 


PRINCIPLES     OF    MECHANICS    AS    APPLIED 
TO   THE   SOLAR   SYSTEM. 


FORCE    OF    THE    SUN. 

The  comparative  sizes  of  the  Sun,  Jupiter,  the  Earth  and 
the  Moon,  as  shown  in  Figure  I,  are  intended  to  give  an 
idea  of  the  power  and  force  of  the  Sun  as  acting  upon  the 
planets  from  the  center  of  the  solar  system.  The  propor- 
tional size  of  the  Moon  is  shown  only  where  the  figures  of 
Jupiter  arid  the'Earth  are  enlarged.  The  diameter  of  the 
Sun.  as  shown,  is  sufficiently  large  to  include  about  ten 
diameters  of  Jupiter  when  placed  in  a  straight  line,  and  the 
diameter  of  Jupiter  equals  about  eleven  diameters  of  the 
Earth,  while  the  Earth's  diameter  embraces  nearly  four 
diameters  of  the  Moon,  the  diameter  of  which  is  about  two 
thousand  one  hundred  and  sixty  miles.  The  diameter  of 
the  Moon  compares  wrell  with  the  distance  from  San  Fran- 
cisco to  Chicago,  or  from  San  Francisco  to  the  Sandwich 
Islands,  or  to  the  length  of  the  Mediterranean  Sea. 

THEORIES    OF    PLANETARY    MOTION. 

Most  of  the  theories  advanced  by  astronomers,  within 
the  last  two  or  three  centuries,  in  regard  to  planetary  mo- 
tion, position,  etc.,  have  been  accepted  and  readvocated  by 
nearly  all  who  have  followed  them  in  the  study  of  that 
science  dowrn  to  the  present  time,  with  but  few  dissenting 
statements. 

Ptolemy  guided  the  greatest  researchers  in  astronomical 
science  into  error  for  nearly  thirteen  hundred  years;  and 
although  Kepler  was  one  of  the  principal  men  to  break 
through  the  barriers  of  erroneous  traditions  and  beliefs,  yet 
he  retained  a  belief  in  the  music  of  the  spheres,  which  is 
now  conceded  to  be  one  of  the  greatest  fallacies  which  was 


10  MECHANICS    AI'l'LIKI)    TO    THE    SOLAR    SYSTEM. 

attached  to  the  astronomical  science.  Yet  all  that  he  gave 
us  that  is  true  is  just  as  valuable  as  if  he  had  never  advo- 
cated theories  which  have  since  been  discarded.  From  be- 
fore his  time  to  the  present,  many  of  the  theories  have  been, 
are  still,  and  no  doubt  will  remain,  speculative. 

Theories  which  have  been  advanced  to  account  for  the 
various  movements  of  the  planets  and  planetary  substances 
have  not  been  accepted  as  harmonizing  entirely  with  nat- 
ural forces,  and  so  the  cause  of  their  movements  has  been 
only  partially  explained.  The  law  of  attraction  and  gravi- 
tation, as  set  forth  by  authors  generally,  is  almost  univers- 
ally accepted  as  being  correct ;  but  a  plausible  theory  show- 
ing the  development  of  the  repelling  force  and  its  manner 
of  counter-balancing  the  planetary  bodies  and  of  rotating 
them  on  their  axes  and  around  the  Sun,  also  the  satellites 
around  their  primaries,  etc.,  has  heretofore  'been  discourag- 
ingly  sought  for  by  many  earnest  searchers  in  the  science 
pertaining  to  heavenly  bodies. 

The  author  attempts  herein  to  show  the  manner  and  the 
harmony  in  which  the  two  forces  are  acting  together  upon 
the  planetary  bodies  and  substances  where  one  force  is 
always  trying  to  draw  them  to  itself,  while  the  other  is 
always  keeping  them  certain  distances  away. 

The  repelling  force,  as  herein  set  forth  and  illustrated,  is 
claimed  to  be  produced  by  the  centrifugal  force  which  is 
developed  by  the  rotation  of  the  Sun  and  planets  on  their 
axes,  and  which  is  thrown  from  the  equatorial  surfaces  of 
the  revolving  bodies  in  sufficient  amount  to  keep  the  planets 
and  bodies  upon  which  it  is  acting  at  the  various  distances 
at  which  they  are  seen,  and  also  to  rotate  them  on  their 
axes  and  revolve  them  in  their  orbits.  This  same  force  is 
shown  to  be  operating  upon  the  more  distant  planets  in  the 
same  manner,  and  these  are  in  each  case  drawn  by  the  ever- 
net  ing  law  of  attraction,  and  always  met  by  the  repelling 
force  which  causes  their  varying  movements  according  to 
the  amount  and  manner  in  which  this  force  is  applied. 

In  mechanics,  estimates  of  power  required  to  accomplish 
state*  1  results  can  be  made  with  tolerable  accuracy,  with 
margins  for  loss  by  radiation,  friction,  etc.,  which  must 


THE    SUN.  11 

all  be  considered  in  the  economic  result,  or  otherwise,  of  the 
object  to  be  attained ;  but  in  the  solar  system,  there  are  no, 
indications  as  to  the  economy  of  forces,  either  of  attraction 
or  of  repulsion. 

The  power  of  attraction  appears  to  be  a  natural  and  an 
established  force  pervading  all  space  and  the  principal 
agency  by  which  the  substances  of  the  celestial  centers  of 
the  universe  have  been  drawn  together  and  by  which  has 
been  effected  the  building  up  and  sustaining  in  form  of  the 
planetary  and  gaseous  bodies  of  our  solar  system. 

The  repelling  action  of  the  Sun  and  of  the  revolving  plan- 
etary bodies  is  also  a  law  natural  to  them,  for  by  their 
rotation  they  are  always  throwing  off  the  repelling  force, 
whether  a  planetary  body  or  substance  upon  which  it  can 
act  be  Avithin  range  or  not. 

THE  SUN. 

The  Sun  is  the  great  central  body  of  attraction,  light  and 
force  of  this  solar  system,  towards  which  all  of  the  planets 
and  planetary  substances  are  drawn,  and  from  which  they 
are  all  repelled,  and  around  which  they  all  revolve.  It 
attracts  or  draws  to  itself,  in  direct  lines,  by  the  law  of 
attraction,  from  every  direction  in  space  around  it,  from  the 
north  and  south  as  wrell  as  in  the  direction  in  which  the 
planets  are  found.  Its  light  is  presumed  to  radiate  from 
every  part  of  its  surface  in  direct  lines  and  in  equal  quan- 
tity and  brightness  on  its  northern  and  southern  surfaces, 
if  not  more  so  than  on  or  near  the  equator. 

The  Sun  is  about  866,000  miles  in  diameter,  and  rotates  on 
its  axis,  from  west  to  east,  once  in  about  twenty-five  days. 
It  seems  to  be  surrounded  by  a  gaseous  envelope  or  influence 
which  appears  to  adhere  to  it.  The  depth  of  this  envelope 
is  not  known,  but  it  is  probably  extensive,  as  eruptions  have 
been  observed  on  its  surface  which  extended  to  a  height  of , 
more  than  200,000  miles  without  being  disturbed  by  any 
external  influence,  thereby  showing  that  at  that  distance 
from  the  Sun  the  gaseous  envelope  revolves  with  it.  This 
gaseous  influence  which  adheres  to  and  revolves  with  the 
Sun  is  probably  of  greater  depth  in  the  region  of  the  Sun's 


12  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

equator  than  on  its  northerly  or  southerly  surface,  for  it 
would  be  drawn  away  from  the  region  of  the*poles  and 
towards  the  equator  by  the  rotation  of  the  Sun  on  its  axis, 
as  substances  or  influences  always  seek  the  farthest  point 
from  the  axis  of  a  revolving  body  before  being  thrown  off. 

The  development  of  the  repelling  forces  is  caused  by  the 
rapid  rotation  of  the  Sun  on  its  axis.  These  influences  or 
forces  which  are  thrown  off  seem  to  be  drawn  to  the  Sun, 
from  the  space  at  each  side  of  its  equatorial  region,  and 
carried  by  the  Sun's  rotation  to  or  near  the  extreme  edge 
of  the  gaseous  envelope,  at  or  near  the  Sun's  equatorial 
plane,  there  to  be  thrown  off  as  the  repelling  force,  while 
new  influences  or  elements  are  continually  being  drawn  to 
the  Sun  and  replacing  them  only  to  be  thrown  off  in  the 
same  manner.  This  repelling  force  seems  not  only  to  be 
thrown  off  from  the  extreme  edge  of  the  gaseous  envelope, 
but  some  of  it  appears  to  be  developed  and  thrown  out  from 
all  parts  or  distances  between  the  outer  edge  of  it  and  the 
surface  of  the  revolving  body,  and  it  seems  to  permeate 
and  operate  through  any  influences  which  ma}'  be  outside 
of  it. 

Whatever  this  repelling  force  is,  and  whether  acting  singly 
or  combined,  whether  electrical  or  otherwise,  is  not  yet 
known;  but  the  disturbances  of  the  magnetic  needle  wher- 
ever these  forces  are  interfered  with  favor  the  theory  of 
electric  repulsion ;  nor  is  it  yet  known  that  there  are  not 
natural  agents,  yet  undiscovered,  that  will  equal  if  not  excel 
it  in  subtlety,  wonder  and  usefulness. 

There  seems  to  be  nothing  surrounding  the  Sun  or  any 
of  the  planetary  bodies  to  indicate  a  throwing-off  force, 
except  in  the  regions  of  their  equatorial  planes. 

Many  of  the  photographs  of  the  Sun  which  have  been 
taken  during  the  time  of  total  eclipse  show  streams  appar- 
ently leaving  it  in  greater  amount  and  reaching  farther 
from  its  surface  in  the  region  of  the  equator  than  elsewhere. 

The  principle  that  keeps  a  ball  or  sphere  suspended  and 
revolving  in  a  jet  of  air  or  water  when  emitted  vertically 
with  sufficient  force  to  overcome  the  attraction  of  the  Earth 
is  similar  in  action  to  the  force  that  is  constantly  and  sim- 


THE    SUN.  13 

ultaneously  thrown  off  from  the  entire  circumference  of  the 
Sun  and  all  of  the  rotating  planetary  bodies  or  any  rotating 
sphere  at  or  near  their  equators. 

The  principles  of  mechanics  as  herein  applied  and  illus- 
trated are  intended  to  refer,  in  general,  to  the  manner  in 
which  the  repelling  force  is  set  in  motion  and  applied  to 
the  planetary  bodies,  and  to  the  results  as  shown  in  the 
planetary  movements.  It  is  herein  claimed  that  all  of  the 
planetary  bodies,  while  revolving  around  the  Sun  and 
rotating  on  their  axes,  are  only  acting  in  harmony  with  and 
obedient  to  a  superior  force  which  is  naturally  and  mechan- 
ically acquired  and  applied  to  them. 

In  applied  mechanics  it  is  well  known  that  if  the  rotation 
or  motion  of  a  body  which  produces  or  supplies  power  is 
maintained  at  a  regular  and  uniform  speed,  a  steady  and 
uniform  result  will  be  produced  wherever  this  power  is 
so  applied;  but  when  the  force  of  a  power  is  varyingly 
applied,  corresponding  results  are  expected.  So,  the  author 
claims,  in  regard  to  the  planetary  motions,  that  wherever 
varying  motions  of  the  planetary  bodies  are  seen,  we  may 
expect  to  find  the  force  that  keeps  them  in  their  orbits 
applied  to  them  in  a  correspondingly  varying  manner  also. 

As  will  appear  farther  on,  and  as  shown  in  the  sectional 
edge-view  of  the  Sun,  in  Figure  II,  this  force  of  the  Sun  is  not 
equally  applied  to  the  planetary  bodies  during  their  entire 
orbital  circuits,  for  all  planets  cross  this  force  at  a  small 
angle  to  it  twice  in  each  of  their  revolutions  around  the 
Sun,  and  the  superior  amount  of  force  which  is  applied  to 
them  at  times  when  crossing  it  results  in  their  varying 
orbital  distances ;  but  the  rotation  of  the  Sun  and  of  the 
planetary  bodies  on  their  axes  is  probably  uniform  with 
most  of  them,  for  bodies  as  large,  cumbersome  and  heavy  as 
any  of  these  must  have  gained  by  their  rapid  rotations 
so  great  a  momentum  that  other  than  a  uniform  axial  rota- 
tion must  be  an  unnatural  movement. 

The  axes  of  the  Sun  and  of  each  of  the  rotating  planets 
are  maintained  in  their  same  general  directions  by  the 
revolution  of  the  planetary  substance  matter  around  their 
axial  centers.  These  substances  are  moving  in  direct  or 


14  MECHANICS    APPLIED    TO   THE    SOLAR    SYSTEM. 

straight  lines,  excepting  the  regular  curve  which  they 
make  around  their  centers,  according  to  their  radial  dis- 
tances. The  velocity  and  momentum  of  the  planetary 
substances  always  depend  on  the  distances  that  they 
are  from  the  axis  of  revolution.  As  the  entire  amount  of 
the  Earth's  substance  revolves  around  its  axial  center  once 
in  about  twenty-four  hours,  the  velocities  of  this  substance 
vary  all  the  way  from  nothing,  at  the  axis,  to  more  than 
one  thousand  miles  per  hour,  on  the  surface  at  the  equa- 
tor. This  would  indicate  an  average  speed  and  momentum 
which  would  about  equal  that  of  the  Earth,  if  it  were  mov- 
ing in  a  straight  line  with  the  velocity  of  three  or  four 
hundred  miles  per  hour.  The  amount  of  power  required 
to  cause  any  deegree  of  lateral  movement  of  a  body  of  like 
dimensions,  if  going  at  a  velocity  of  three  or  four  hundred 
miles  per  hour,  should  indicate  a  proportional  power  that 
would  be  required  to  change  the  plane  of  the  Earth's  equa- 
tor in  a  corresponding  degree.  This  same  principle  operates 
in  maintaining  the  direction  of  the  axes  of  all  of  the  revolv- 
ing planets,  the  axis  of  the  Sim  and  the  axes  of  all  substances 
whatsoever  which  have  a  rotary  motion,  even  to  the  child's 
spinning-top,  except  that  the  top  is  influenced  more  by 
friction  and  attraction,  which  operate  against  its  move- 
ments. The  top  is  sustained  in  its  tilted  position  by  the 
velocity  at  which  one-half  of  its  volume  is  being  constantly 
moved  contrary  to  the  attraction  of  the  Earth  and  with  a 
speed  and  momentum  which  exceed  the  Earth's  attraction 
for  it,  and  as  there  are  only  the  centrifugal  force  of  the  top 
and  the  attraction  of  the  Earth  as  the  principal  forces  in 
operation  connected  with  it,  it  may  revolve  in  a  tilted  po- 
sition until  its  speed  decreases  to  a  degree  at  which  the  at- 
traction of  the  Earth  exceeds  the  centrifugal  force  of  the 
top,  at  which  time  it  will  suddenly  fall.  The  natural  ten- 
dency of  the  top,  while  in  motion,  is  to  gradually  assume  a 
vertical  axial  position.  The  principle  of  maintaining  a 
general  axial  direction  is  also  shown  by  the  fact  that  a  heavy 
top  will  resist  considerable  force,  when  rotating  rapidly,  if 
an  effort  be  made  to  quickly  change  its  plane  of  rotation. 
(See  'Scientific  American,  October  9th,  1886,  page  230.) 


THE  srx.  17 

The  Sun  and  each  revolving  planet  are  developing  and 
throwing  off  this  repelling  force  or  influence  at  the  region 
of  their  equators  and  in  the  direction  of  their  equatorial 
planes,  and  in  amount,  according  to  the  influence  which 
surrounds  them,  with  a  steady  and  uniform  current,  and 
with  a  force  according  to  their  individual  axial  velocities. 
This  repelling  force,  put  in  motion  by  the  Sun,  is  presumed 
to  extend  from  the  Sun  far  into  the  space  beyond  the  planet 
Neptune,  while  the  force  developed  by  the  planets  extends 
from  them  considerably  beyond  the  orbits  of  their  most 
distant  satellites,  as  shown  in  Figure  IV. 

It  is  intended  to  illustrate  in  the  sectional  side  and  edge- 
view  of  a  part  of  the  planetary  system,  as  shown  in  Figure 
II,  the  manner  in  which  the  Sun's  force  is  distributed  by  its 
rotation  and  the  manner  in  which  the  influences  approach 
the  Sun;  also  the  positions  of  some  of  the  planets  as  being 
acted  upon  and  controlled  by  the  Sun's  force.  In  the  sec- 
tional edge-view,  the  poles  of  some  of  the  planets  are  shown 
in  positions  similar  to  those  of  the  Earth  at  the  time  of  the 
Summer  and  Winter  solstices,  while  the  equatorial  plane  of 
the  Sun  is  represented  by  a  dotted  line  in  position  similar 
to  its  relative  angle  to  the  ecliptic  at  its  equinoxes.  The 
angles  of  all  of  the  orbits  are  shown  as  varying  in  degree  from 
the  Sun's  equatorial  plane.  The  ecliptic,  or  the  plane  or 
level  of  the  Earth's  orbit,  is  shown  by  being  extended  with 
dotted  lines.  From  this  plane,  astronomers  take  measure- 
ments in  the  heavens.  In  other  respects,  it  has  no  more 
significance  than  the  orbit  of  any  other  planet,  as  nearly  all 
of  the  varying  movements  of  the  planets  depend  on  the 
extent  of  the  Sun's  force  as  applied  to  them.  If  the  planets 
were  observed  and  studied  as  intersecting  the  plane  of  the 
Sun's  force,  also  the  satellites  as  intersecting  the  equatorial 
planes  of  their  primaries,  much  information  might  be 
gained  that  would  lead  to  a  knowledge  of  planetary  action 
that  cannot  be  so  easily  obtained  by  only  a  knowledge  of 
the  intersection  of  them  with  the  ecliptic. 

In  the  sectional  side-viewTs,  are  seen  the  Sun  and  planets 
in  their  respective  positions*  and  all  rotating  on  their  axes, 
from  west  to  east,  the  planets  traveling  around  the  Sun  in 


18  ME(  HANH  S    Al'I'LIED    TO    THE    SoLAK    SYSTEM. 

the  same  direction.  In  the  same  views  are  shown  dotted 
lines  representing  the  direction  of  the  attraction  of  the  Sun 
for  the  planets,  as  extending  from  the  center  of  each  planet 
to  the  center  of  the  Sun.  and  lines  representing  repulsion 
extending  in  tangents  from  the  Sun  to  the  planets.  By  tin- 
aid  of  this  illustration,  it  can  be  seen  that  much  more  force 
is  being  applied  to  one  and  the  same  side  of  the  line  of 
attraction  of  all  or  each  of  the  planets  than  to  the  other 
side.  If  this  repelling  force  is  powerful  enough  to  keep 
them  all  at  their  respective  orbital  distances,  then  it  seems 
evident  that  it  is  also  powerful  enough  to  rotate  them  all  on 
their  axes  in  the  direction  of  least  resistance  and  in  their 
orbits  in  the  same  direction. 

MOTIONS  OP   THE   SUN. 

Spots  have  been  observed,  apparently  crossing  the  Sun's 
surface,  by  which  the  time  of  its  axial  rotation  has  been 
ascertained.  At  about  the  time  of  the  Winter  solstice,  or 


near  the  end  of  the  year,  the  spots  appear  to  travel  straight 
across  the  Sun,  ascending  a  little  as  they  advance,  as  shown 
in  the  diagram  at  "A,"  Figure  III.  When  observed  toward 
the  last  of  March,  or  about  the  time  of  the  Vernal  equinox, 
the  spots  appear  to  travel  across  the  Sun  in  a  somewhat 
bowed  path,  causing  them  to  appear  to  rise  and  fall  a  little 
while  crossing  the  Sun  as  shownat"B."  At  the  time  of 
the  Summer  solstice,  or  near  the  last  of  June,  they  are  seen 
t<j  travel  straight  across  the  Sun  again,  descending  a  little 
as  they  advance,  as  shown  at  "  <  .  When  observed  from 
the  direction  of  the  Autumnal  equinox,  or  near  the  last  of 
September,  they  appear  to  descend  and  rise  a  little  as  thev 


MOTIONS    OF    THE    SUN.  10 

advance,  as  shown  at  "  B."  The  changes  which  appear  to 
occur  in  the  paths  of  the  spots  in  crossing  the  Sun  are  pro- 
duced gradually,  only  reaching  the  extremes  at  about  the 
times  stated  above,  and,  if  observed  at  any  intermediate 
time,  they  would  appear  dipped  or  bowed  in  proportion  to 
and  according  to  the  time  in  which  they  are  observed. 
These  paths  show  the  equatorial  plane  of  the  Sun  to  be  at  an 
angle  of  about  seven  degrees  to  the  ecliptic.  The  spots 
appear  more  abundantly  in  periods  of  about  eleven  years, 
while  at  intermediate  periods  they  sometimes  almost,  if  not 
quite,  disappear.  Sometimes  some  of  the  spots  are  of  short 
duration,  often  less  than  half  an  hour,  while  some  do  not 
wholly  disappear  until  six  or  seven  months  after  their 
appearance.  Spots  are  seldom  seen  within  less  than  five 
or  beyond  thirty-five  degrees  latitude  each  side  of  the  Sun's 
equator. 

There  is  no  cause  yet  assigned  for  the  periodicity  of  the 
Sun's  spots.  It  may  be  found  to  be  only  a  succession  of 
natural  reactions  within  itself,  where  one  extreme  follows 
another,  the  same  as  often  seen  upon  the  Earth,  or  it  may 
be  found  to  be  a  tidal  effect,  caused  by  the  rotation  on  its 
axis  when  affected  by  the  attraction  of  some  of  the  planets. 

The  Sun  is  also  revolving  around  a  common  center,  which 
is  always  within  itself.  It  is  also  said  to  be  traveling 
toward  the  constellation  Hercules  at  a  rate  of  more  than 
a  hundred  and  fifty  million  miles  a  year,  but  the  location  of 
the  center  of  the  force  or  power  which  propels  it,  aside  from 
Deity,  has  not  yet  been  determined. 

Besides  attracting  new  forces,  or  influences,  as  the  Sun 
and  planets  are  traveling  along  through  the  heavens,  this 
force,  which  is  continually  being  thrown  off  from  the  Sun 
and  planets  at  and  near  their  equators,  is  evidently  nearly 
all  attracted  back  to  them  soon  again,  and  as  rapidly  and 
nearly  as  great  in  quantity  as  that  which  was  thrown  off, 
but  towards  a  much  larger  surface  which  is  at  each  side  of 
the  equatorial  planes.  Some  of  this  force  is  returning  con- 
tiguous, some  adjacent  and  some  quite  remote  from  the 
stream  which  is  being  thrown  off.  Much  of  it  which  is 
returning  contiguous  to  the  stream  is  drawn  into  it  again 


20  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

by  eddies  which  are  continually  forming,  and  there  carried 
away  again  before  getting  near  the  body  which  attracts  it. 
The  disturbances  of  the  magnetic  needle  indicate  currents 
which  correspond  to  the  action  of  the  Sun's  force  at  its  sur- 
face, in  passing  from  toward  the  poles  of  the  Earth  to  the 
equator,  but  never  from  the  equator  toward  the  poles.  A 
possible  corresponding  effect  may  be  seen  in -the  Aurora 
Borealis,  or  Northern  Lights,  as  well  as  the  Zodiacal  Light, 
as  seen  in  the  tropics,  the  latter  of  which  may  be  due  to  the 
action  of  the  Sun's  instead  of  the  Earth's  force.  This  action 
of  the  Sun  and  planets  gives  us  a  system  which  admits  of 
the  forces  or  influences  being  used  over  and  over  again,  and 
which  clears  the  space  of  planetary  matter,  as  it  becomes 
secured  to  the  planets  and  Sun  by  their  attraction  when- 
ever passing  near  enough  to  each  other,  thus  ever  main- 
taining a  firmament  in  the  heavens  and  limiting  the  calcu- 
lations of  the  time  of  worldly  or  planetary  existence  to  the 
Infinite  Ruler  of  the  Universe. 

MERCURY. 

Mercury,  as  shown  in  Figures  II  and  IV,  is  the  nearest 
known  planetary  body  to  the  Sun.  Its  diameter  is  about  three 
thousand  miles,  and  it  travels  once  around  the  Sun,  from 
west  to  east,  in  about  eighty-eight  days.  It  rotates  on  its 
axis,  from  west  to  east,  once  in  twenty-four  hours  and 
about  five  minutes.  It  has  an  orbital  velocity  of  about  sev- 
enteen hundred  miles  per  minute,  and  travels  at  an  average 
distance  from  the  sun  of  about  thirty-five  million  five  hun- 
dred thousand  miles,  and  in  an  orbit  which  is  more  ellip- 
tical than  any  of  the  orbits  of  the  principal  planets,  its  least 
distance  being  about  twenty-eight  million  one  hundred  and 
fifty  thousand  miles,  while  its  greatest  distance  from  the  Sun 
is  about  forty-three  million  miles.  Its  orbit  is  inclined 
about  seven  degrees  to  the  ecliptic,  being  more  than  twice 
the  amount  of  the  inclination  of  the  orbits  of  any  of  the 
rest  of  the  principal  planets. 

When  it  is  in  perihelion,  or  its  nearest  approach  to  the 
Sun,  it  is  much  nearer  the  Sun  than  it  is  natural  for  it  to 
remain,  for  the  repelling  force  of  the  Sun  at  Mercury's 


VENUS.  23 

perihelion  distance  considerably  exceeds  ;the  attraction  of 
the  Sun  for  the  planet,  and  so  it  is  gradually  borne  farther 
away  from  the  Sun  while  moving  along  in  its  orbit;  while, 
at  the  same  time,  the  momentum  which  it  received  when  it 
was  approaching,  and  when  in,  and  near  its  perihelion,  nowr 
aids  the  Sun's  force  in  carrying  it  to  its  aphelion,  or  to  the 
farthest  part  of  its  orbit  from  the  Sun,  at  which  distance  it 
is  beyond  its  mean  place  and  where  the  attractive  force  of 
the  Sun  for  the  planet  exceeds  the  repelling  force  of  the  Sun. 
After  the  planet  leaves  its  perihelion  it  gradually  loses  its 
speed  and  momentum  until  it  arrives  at  its  aphelion. 
When  traveling  from  aphelion  to  perihelion  it  is  gradually 
drawn  a  little  nearer  to  the  Sun  by  the  excess  of  the  Sun's 
attraction  over  its  repelling  force,  thus  gaining  speed  and 
momentum  in  proportion  until  it  arrives  at  its  perihelion 
again.  The  momentum  that  it  has  gained  or  acquired 
since  leaving  its  aphelion  carries  it  nearer  to  the  Sun  again 
than  its  mean  place,  and  so  it  is  thrown  off  as  before,  and 
always  in  an  elliptical  orbit. 

VENUS. 

Next  to  Mercury,  we  have  the  planet  Venus,  as  shown  in 
Figures  II  and  IV.  Its  diameter  is  about  seven  thousand 
seven  hundred  and  fifty  miles,  and  it  travels  once  around 
the  Sun  in  about  two  hundred  and  twenty-four  and  three- 
fourths  days,  at  an  average  distance  of  about  sixty-seven 
millions  of  miles  from  the  Sun,  and  in  an  orbit  which  is 
nearly  circular.  Its  ellipticity  is  said  to  be  only  about  nine 
hundred  thousand  miles.  Venus  travels  with  an  orbital  ve- 
locity of  but  little  more  than  thirteen  hundred  miles  per  min- 
ute, and  with  its  poles  greatly  inclined  to  the  ecliptic,  while 
its  orbit  is  inclined  to  the  ecliptic  only  three  degrees  and 
about  twenty-three  and  a  half  minutes.  It  seems  that  it  is 
to  the  thro  wing-off  force  of  the  Sun  that  we  should  look  for 
the  cause  of  its  orbit  being  so  nearly  circular.  If  the  Sun's 
force  at  its  perihelion  exceeds  the  attraction  of  the  Sun  for 
the  planet  but  little,  it  is  evident  that  the  Sun  would  have 
but  a  short  distance  to  force  it  away  before  the  attraction 
and  throwing-off  force  of  the  Sun  would  be  equal,  and  it 


24  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

could  only  go  the  distance  beyond  its  mean  distance  that 
the  excess  of  the  Sun's  force  over  the  Sun's  attraction,  when 
at  perihelion,  would  send  it,  and  the  momentum  gained  or 
acquired  on  its  return  from  its  aphelion  would  be  so  little 
that  it  could  get  but  little  closer  to  the  Sun  at  its  perihelion 
than  its  average  distance  in  its  orbit.  Thus  we  see  that  this 
law,  as  in  the  case  of  Mercury,  would  cause  the  small  ellip- 
ticity  of  the  orbit  of  Venus. 

If  the  Sun  should  remain  in  one  position  and  Venus  should 
travel  around  it  in  the  direct  line  of  the  Sun's  force,  we  might 
expect  that  an  equal  force  of  the  Sun  would  keep  Venus  at  an 
equal  distance  in  its  entire  circuit.  But,  as  the  Sun  is  trav- 
eling through  the  heavens  at  an  immense  velocity  and  tak- 
ing all  of  the  planets  along  with  it,  it  would  be  in  harmony 
with  this  law  to  presume  that  when  Venus  passes  between 
the  Sun  and  the  point  toward  which  the  Sun  is  traveling, 
it  would  be  a  little  nearer  the  Sun  at  that  point  and  a 
little  farther  from  the  Sun  when  on  the  opposite  side,  for,  in 
the  first  instance,  the  Sun  would  be  in  the  act  of  approach- 
ing Venus,  and  in  the  second  it  would  be  in  the  act  of  leav- 
ing it,  which  might  make  the  planet's  orbit  perceptibly 
elliptical.  The  question  often  arises  whether  or  not  we 
should  take  into  consideration  the  movements  and  positions 
of  the  planets,  in  determining  their  specific  gravity,  etc.; 
for  we  see  the  planet  Mercury  plunging  into  the  Sun's 
force  and  then  being  thrown  correspondingly  away,  while 
Venus  is  gently  drawn  to  a  position  where  the  force  is  at  all 
times  nearly  equally  applied.  This  seems  to  be  plainly 
shown  by  the  inclination  of  the  orbit  of  Venus  to  the  eclip- 
tic, which  is  only  three  degrees  and  about  twenty-three  and 
a  half  minutes.  As  before  stated,  the  greatest  inclination 
of  the  plane  of  the  Sun's  equator  is  supposed  to  be  a  little 
more  than  seven  degrees  to  the  ecliptic,  which  is  best  seen 
about  the  twenty-first  of  March,  at  which  time  the  Earth  is 
the  farthest  below,  or  south  of,  the  Sun's  equatorial  plane,  and 
about  the  twenty-first  of  September,  when  the  Earth  has 
reached  the  point  which  is  farthest  north  of  the  Sun's  equa- 
torial plane,  or  force  line.  The  center  of  the  Sun's  force  is  then 
passing  about  seven  degrees  below,  or  south  of,  the  Earth. 


VENUS.  25 

When  the  ascending  node  of  Venus  occurs  in  that  part  of 
its  orbit  which  corresponds  to  the  Earth,  when  nearing  the 
middle  of  December,  it  crosses  the  Sun's  force  in  nearly  the 
same  relative  position  in  which  the  Earth  does,  and  when  it 
travels  around  in  its  orbit  until  it  gets  to  a  point  which 
nearly  corresponds  to  our  Vernal  equinox,  it  is  about  three 
and  a  half  degrees  north  of,  or  above,  the  plane  of  the  ecliptic, 
and  south  of,  or  below  the  Sun's  equatorial  plane,  which 
would  place  Venus  within  about  three  and  a  half  degrees 
of  the  center  of  the  Sun's  force.  That  is  the  greatest  dis- 
tance away  from  it  that  the  planet  Venus  ever  gets.  The 
same  conditions  occur  on  the  opposite  side  of  the  orbit  in 
the  relative  position  to  our  Autumnal  equinox,  except  that 
Venus  is  about  three  and  a  half  degrees  above,  or  north  of, 
the  Sun's  equatorial  plane,  instead  of  below  it. 

An  extract  from  the  Mining  and  Scientific  Press  of  Novem- 
ber 13,  1880,  adds  more  proof  of  the  active  principle  of  this 
force,  as  will  be  seen  by  the  perusal  of  the  following : 

"Mr.  R.  G.  Jenkins,  F.  R.  A.  S.,  has  endeavored  to  show 
"  a  very  remarkable  effect  of  the  planet  Venus  upon 
"  the  Earth.  The  present  British  Astronomer  Royal 
"  proved,  many  years  ago,  that  the  disturbing  effect  of 
"  this  planet  was  so  great  that  the  Earth  was  mate- 
"  rially  pulled  from  its  orbit.  Mr.  Jenkins  shows  that 
"  it  is  to  this  action  that  we  must  look  for  an  explanation 
"  of  the  cold  waves  which  occur  on  an  average  every  eight 
"  years,  as  in  1829,  1837,  1845,  1855,  1863, 1871,  1879,  and 
"  that  for  the  next  fifty  years  the  temperature  will  be  below 
"  the  average.  He  states  that  a  heat  wave  has  been  ob- 
"  served  to  pass  over  the  Earth  every  twelve  years,  nearly 
"  cotemporary  with  the  arrival  of  the  planet  Jupiter  at  its 
"  perihelion,  such  a  wave  being  now  close  at  hand."  * 

By  reference  to  Figures  II  and  IV  it  will  be  seen  that  when 
the  planet  Venus  passes  between  the  Earth  and  the  Sun  that 
considerable  of  the  force  of  the  Sun  must  be  intercepted 
that  would  have  acted  upon  the  Earth.  When  the  Sun's  re- 
pelling force,  as  applied  to  the  Earth,  is  partially  diminished 
by  the  interception  of  the  planet  Venus,  the  Earth  falls 


26  MECHANICS   APPLIED    TO    THE   SOLAR   SYSTEM. 

toward  the  Sun  in  proportion,  and  may  also  be  attracted  a 
little  by  Venus  at  the  same  time,  but  as  soon  as  Venus 
passes  along  so  as  to  leave  the  Earth  exposed  to  the  full 
force  of  the  Sun,  the  Earth  is  thrown  back  again  to  its  nat- 
ural orbital  distance.  If  an  increased  amount  of  the  Sun's 
rays  will  supply  an  increased  amount  of  heat,  a  cold  wave 
would  be  the  natural  result  when  such  rays  were  inter- 
cepted and  diminished.  It  is  the  general  belief  that  the 
nearer  the  Earth  is  to  the  Sun,  the  greater  will  be  the  heat 
furnished  by  the  Sun.  But,  in  this  instance,  when  the  Earth 
is  drawn  materially  nearer  the  Sun,  the  heat  of  the  Sun  is 
sensibly  diminished. 

The  heat  wave  to  which  the  eminent  astronomer  refers, 
in  connection  with  the  planet  Jupiter,  is  only  another  nat- 
ural result  that  might  be  expected  to  follow  those  condi- 
tions, for  the  force  that  is  required  to  repel  the  planet 
Jupiter  and  roll  it  on  in  its  orbit  must  be  very  great,  and  as 
this  force  extends  in  straight  lines  from  the  Sun  to  the  objects 
which  it  repels,  no  doubt  this  force  is  more  compressed  in 
the  direction  of  any  resistance  than  where  it  has  free  exit 
from  the  Sun,  and  while  the  Earth  is  passing  through  a  re- 
gion of  this  compressed  force  an  increased  temperature  on 
the  Earth's  surface  would  be  the  more  natural  result. 

EARTH. 

The  Earth  is  also  shown,  in  Figures  II  and  IV,  as  the  third 
planet  from  the  Sun.  It  makes  one  orbital  revolution  in 
about  three  hundred  and  sixty-five  and  a  fourth  days,  at  an 
average  distance  from  the  Sun  of  about  ninety-three  million 
miles,  in  an  orbit  somewhat  elliptical,  and  to  which  the 
Sun's  equatorial  plane  is  inclined  about  seven  degrees,  as 
before  stated.  Its  axis  is  inclined  to  its  orbit,  or  ecliptic, 
about  twenty-three  and  a  half  degrees,  and  it  rotates  on  its 
axis  once  in  twenty-three  hours  fifty-six  minutes  and  about 
four  seconds.  By  comparing  the  conditions  and  motions  of 
the  Earth  with  those  of  Mercury  and  Venus,  it  is  obvious 
that  it  must  also  be  controlled  by  the  same  force  and  in  about 
the  same  manner,  for  when,  in  that  part  of  its  orbit  farthest 
from  the  Sun  (toward  the  last  of  June),  it  appears  to  be  in 


EARTH. AXIAL    INCLINATIONS.      '  27 

the  direct  line  of  the  Sun's  force,  or  equator,  as  the  spots  on 
the  Sun  appear  to  travel  straight  across  the  Sun's  surface, 
and  when  it  reaches  its  autumnal  equinox  it  gets  so  far  to 
the  north  of  the  Sun's  equatorial  plane  that  the  spots  in 
passing  across  the  Sun  Appear  to  descend  and  rise  to  an  ex- 
tent that  would  indicate  that  the  Earth  is  about  the  before- 
mentioned  seven  degrees  to  the  north  of  the  Sun's  equa- 
torial force  line.  This  allows  the  Earth  to  be  drawn  a  little 
nearer  to  the  Sun  and  to  gain  a  little  in  velocity,  which  con- 
tinues until  it  arrives  at  its  perihelion  and  in  the  direct  line 
of  the  Sun's  equatorial  force  again,  as  indicated  by  the  spots 
appearing  to  pass  straight  across  the  Sun's  surface.  In  this 
part  of  its  orbit  it  is  nearer  to  the  Sun  than  its  average  dis- 
tance. The  Sun's  force  there  exceeds  the  Sun's  attraction 
for  the  Earth,  and,  as  it  passes  along  in  its  orbit,  it  loses 
speed  and  momentum,  and  is  borne  gradually  a  little 
farther  away  by  the  excess  of  the  Sun's  force,  as  in  the  case 
of  the  planet  Mercury.  When  it  arrives  at  its  Vernal  equi- 
nox the  spot  lines  which  cross  the  Sun  appear  bowed  a  little, 
showing  that  the  Sun's  greatest  equatorial  force  was  passing 
a  little  above  or  north  of  the  Earth,  at  that  point  of  its 
orbit.  As  it  passes  on  from  here  it  continues  to  lose  its 
orbital  velocity  and  momentum  until  it  reaches  its  aphe- 
lion, thus  completing  one  orbital  revolution. 

AXIAL    INCLINATIONS. 

The  inclination  of  the  poles  of  the  planets  to  their  orbits 
may  be  due  to  one  polar  hemisphere  being  heavier  than  the 
other  and,  consequently,  more  affected  by  the  attraction  of 
the  Sun,  when  in  the  more  distant  part  of  their  orbits  or 
where  the  Sun's  attractive  exceeds  its  repelling  force  for  the 
planet.  As  the  Earth  attracts  the  heavier  side  of  the  Moon 
toward  itself,  so  the  Sun,  according  to  the  same  law,  may 
attract  the  heavier  part  of  the  planets  toward  itself,  and  the 
inclination  of  the  poles  of  the  planets,  to  their  orbits,  may 
indicate  the  degree  to  which  they  are  unbalanced  in  form 
or  attractive  properties,  Jupiter  showing  a  nearly  balanced 
and  Venus  a  greatly  unbalanced  condition.  We  know  that 
the  northern  hemisphere  of  the  Earth  is  heavier  than  the 


28  MECHANICS    APPLIED    TO    THE   SOLAR    SYSTEM. 

southern,  in  proportion  as  the  amount  of  the  earthy  matter  of 
the  northern  exceeds  that  of  the  southern  hemisphere  in 
volume.  It  may  be  shown  that  it  is  the  unequal  degree  of 
the  Sun's  repelling  and  attractive  influences,  as  acting  upon 
the  Earth  in  connection  with  the  "Moon's  attraction  while 
the  Earth  is  in  different  parts  of  its  orbit,  that  causes  a 
gyratory  movement  of  the  Earth's  North  Pole  and,  as  a 
change  of  the  direction  of  the  Earth's  North  Pole  implies  a 
change  in  the  plane  of  the  Earth's  rotation,  also  the  direc- 
tion of  its  throwing-off  force,  a  shifting  of  the  Moon's  nodes 
on  the  ecliptic  might  follow,  as  a  natural  result,  when  the 
Moon  is  seeking  its  natural  position  in  relation  to  the 
Earth's  repelling  force. 

THE  MOOX. 

The  Earth's  satellite,  or  Moon,  is  about  two  thousand  one 
hundred  and  sixty  miles  in  diameter,  and  at  a  mean  dis- 
tance of  about  two  hundred  and  thirty-eight  thousand 
miles  from  the  Earth.  Its  motions,  in  its  orbit,  are  prob- 
ably as  complex  as  those  of  any  of  the  primary  or  second- 
ary planets  of  our  solar  system.  It  makes  one  revolution 
around  the  Earth,  with  respect  to  the  Sun,  in  about  twenty- 
nine  and  a  half  days,  and  also  one  revolution  on  its  axis  in 
the  same  time,  and  a  little  more  than  twelve  and  a  quarter 
revolutions,  around  the  Earth,  in  one  year.  Its  orbit  is 
quite  elliptical,  the  distance  of  the  Moon  varying  from  about 
two  hundred  and  twenty-six  thousand  to  two  hundred 
and  fifty-one  thousand  miles  from  the  Earth.  It  seldom 
makes  two  revolutions  around  the  Earth  in  the  same  time 
in  the  same  year,  the  time  varying  from  a  few  minutes  to 
several  hours  in  every  year,  until  after  about  eighteen 
years,  when  we  expect  the  same  conditions  to  occur  again. 
Nor  are  any  two  quarter  moons  of  the  same  duration. 
Sometimes  the  Moon  passes  from  quarter  to  quarter  in 
about  six  and  one-half  days,  while  at  other  times  it  re- 
quires as  much  as  eight  and  one-quarter  days,  and  often- 
times in  the  same  year. 

In  the  accompanying  diagram  is  shown,  as  near  as  pro- 
portions will  conveniently  allow,  the  path  of  the  Moon 


THE    MOON.  31 

crossing  and  recrossing  the  orbit  of  the  Earth  during  the 
years  1888  and  1889 ;  also  the  positions  of  the  Moon  in  its 
new  and  full  moon,  and  markings  on  the  Earth's  orbit  show- 
ing the  position  of  the  Earth  when  the  Moon  is  crossing  the 
Earth's  orbit  just  in  the  rear  of  the  Earth  at  the  time  of  the 
first  quarter,  and  the  position  of  the  Earth  when  the  Moon 
crosses  the  Earth's  orbit  just  in  advance  or  ahead  of  the 
Earth  at  the  time  of  its  last  quarter.  The  path  of  the  Moon 
along  the  Earth's  orbit  is  slightly  scolloped,  it  deviating 
from  a  straight  line,  or  from  the  Earth's  orbit,  only  about 
one  mile  in  twenty,  or  two  hundred  and  thirty-eight  thou- 
sand miles  in  the  distance  that  the  Earth  travels  in  its  orbit 
during  the  time  from  first  quarter  to  full  moon,  with  the 
two  hundred  and  thirty-eight  thousand  miles  added,  which 
the  Moon  must  gain  on  the  Earth  during  that  time.  The 
distance  is  sometimes  more  or  less  to  the  mile  than  stated. 
If  the  Moon  when  nearest  the  Earth,  or  when  in  perigree, 
is  about  the  time  of  being  new  or  of  appearing  full,  the  de- 
viation is  less,  and  when  the  Moon  is  in  apogee  in  corres- 
ponding time,  its  deviation  is  more.  The  points  of  perigee 
and  apogee  are  not  fixed  in  its  orbit  with  relation  to  the 
Sun  or  Earth,  but  are  steadily  advancing,  making  an  entire 
revolution  on  the  Moon's  orbit  in  eight  years  and  about  two 
hundred  and  eighteen  days.  At  the  time  of  new  moon 
the  Moon  passes  between  the  Earth  and  the  Sun.  The 
Moon  is  in  or  near  the  Earth's  orbit  when  it  appears  about 
half  full,  the  quarter  after  each  new  moon  being  the  first 
quarter  and  the  quarter  preceding  the  new  moon  being  the 
last  quarter,  both  of  which  occur  while  the  Moon  is  on  the 
inside  of  the  Earth's  orbit,  or  between  the  Earth's  orbit  and 
the  Sun.  When  the  Moon  is  on  the  opposite  side  of  the 
Earth  from  the  Sun,  we  see  nearly  the  entire  surface  that 
the  Sun  shines  upon.  It  is  then  full  moon,  and  the  quarter 
before  the  full  moon  is  the  second  quarter,  and  the  quarter 
after  the  full  moon  is  the  third  quarter,  both  occurring 
while  the  Moon  is  outside  of  the  Earth's  orbit.  During  the 
year  of  1888  the  Moon  was  more  than  four  days  more  time 
on  the  inside  than  on  the  outside  of  the  Earth's  orbit,  and 
during  the  year  1889  it  will  be  about  nine  and  a  half  days 


32  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

more  time  inside  than  outside  of  it.  And,  although  during 
the  twelve  complete  moons  from  new  to  new,  in  1889,  the 
Moon  is  more  than  five  and  a  fourth  days  more  time  inside 
than  outside  of  the  Earth's  orbit,  yet  it  travels  along  the 
Earth's  orbit  nearly  a  million  more  miles  on  the  outside 
than  on  the  inside  of  it,  owing  to  the  fact  that  it  must  gain 
twice  the  distance  that  it  is  from  the  Earth  during  the  sec- 
ond and  third  quarter  of  each  Moon,  or  each  revolution 
around  the  Earth.  When  the  Moon  is  new,  or  directly  be- 
tween the  Earth  and  the  Sun,  its  form  and  surface  mark- 
ings are  faintly  shown  by  the  sunlight  that  is  reflected  from 
the  Earth  back  to  it.  At  that  time  the  Earth  would  appear 
round  or  full,  if  observed  from  the  Moon,  and  when  the 
Moon  is  full,  the  Earth  being  between  the  Moon  and  the 
Sun,  would  appear  as  the  new  moon,  except  that  the  Earth 
would  appear  much  larger  and  the  surface  much  more  dim, 
owing  to  the  small  amount  of  light  that  the  Moon  would 
reflect  back  to  the  Earth. 

When  the  Moon  is  at  first  quarter  it  is  in  the  act  of 'cross- 
ing the  Earth's  orbit  going  from  the  inside  to  the  outside  of 
it,  and  when  in  that  position  we  see  only  one-half  of  that 
half  of  the  Moon  that  the  Sun  shines  upon,  causing  it  to 
appear  half  full,  or  at  first  quarter.  If  the  Earth  could  be 
seen  from  the  Moon  at  that  time,  it  would  appear  to  be  half 
full,  also,  and  as  the  quarter  after  the  full  moon,  or  last 
quarter.  Although  the  Earth  is  traveling  in  \ts  orbit  at 
the  rate  of  about  one  thousand  one  hundred  and  ten  miles  per 
minute,  the  Moon  must  gain  its  average  distance  after  the 
first  quarter,  or  about  two  hundred  and  thirty-eight  thousand 
miles  on  the  Earth,  before  it  can  appear  as  full  moon ;  and 
from  there  it  must  continue  to  gain,  until  it  crosses  from 
the  outside  to  the  inside  of  the  Earth's  orbit,  which  is  about 
two  hundred  and  thirty-eight  thousand  miles,  and  directly 
in  front  of,  or  in  advance  of  the  Earth,  at  which  time  we 
see  only  one-half  of  that  part  of  the  surface'  of  the  Moon 
that  the  Sun  shines  upon,  and  which  completes  the  third 
quarter.  From  here  it  travels  ahead  of  the  Earth,  grad- 
ually getting  to  one  side  and  also  slackening  its  speed,  until 
the  Earth  has  caught  up  with  it  in  relation  to  the  Sun, 


THE    MOON.  33 

when  it  appears  directly  between  the  Earth  and  the  Sun,  or  at 
new  moon,  which  completes  its  fourth  or  last  quarter.  From 
the  position  of  new  moon  it  is  gradually  drawn  back  to  the 
Earth's  orbit,  or  at  first  quarter,  and  with  an  accelerating 
speed  corresponding  to  the  decreasing  speed  of  the  fourth 
quarter.  It  should  be  observed  here  that  the  Moon  has  to 
lessen  its  speed  only  a  very  little  during  the  fourth  and  first 
quarters  in  order  that  the  Earth  may  pass  it,  for  the  Earth 
during  these  two  quarters  travels  nearly  twenty-two  and 
three-quarter  million  miles  in  its  orbit,  and  only  has  to  gain 
twice  the  distance  of  the  Moon  from  the  Earth,  or  less  than  four 
hundred  and  eighty  thousand  miles.  The  speed  of  the  Earth 
in  its  orbit  may  be  pretty  well  realized  by  reference  to  the 
position  of  the  Moon  at  the  last  of  the  third  or  beginning  of 
the  fourth  quarter,  when  it  is  one-half  full ;  as  it  is  then  on, 
or  directly  in,  the  line  in  which  the  Earth  is  traveling  in  its 
orbit,  and  at  a  point  to  which  it  takes  the  Earth  only  about 
three  and  a  half  hours  to  arrive.  As  the  Moon's  orbit  is 
not  parallel  with  the  Earth's,  but  inclined  about  five  de- 
grees to  it,  the  Moon  crosses  and  recrosses  this  plane  or 
ecliptic  twice  in  each  revolution  around  the  Earth.  The 
point  in  its  orbit  where  it  descends  from  above,  or  north  of 
the  ecliptic,  to  below,  or  south  of  it,  is  called  the  descend- 
ing node.  And  the  point  in  its  orbit  which  intercepts  the 
ecliptic  when  it  is  passing  from  below,  or  south  of  the 
ecliptic,  to  the  region  above  it  is  called  the  ascending  node. 
These  points  of  intersections  are  not  fixed  in  the  Moon's 
orbit,  but  occur  a  little  farther  to  the  West  at  each  succeed- 
ing revolution  of  the  Moon  around  the  Earth,  and  are  called 
the  retrograde  movement  of  the  nodes.  They  make  an>n- 
tire  revolution  on  the  orbit  of  the  Moon  in  eighteen  years 
and  about  two  hundred  and  nineteen  days.  The  Moon 
presents  nearly  the  same  surface  to  the  Earth  all  the  time, 
which  is  said  to  be  owing  to  the  fact  that  the  central  point 
of  attraction  upon  which  the  Earth  is  acting  in  the  Moon 
is  a  little  nearer  to  the  side  of  the  Moon  which  is  turned 
toward  the  Earth.  The  side  of  the  Moon  which  is  con- 
stantly presented  to  the  Earth  is  thought  to  be  considerably 
the  heavier,  the  reason  for  which  is  yet  speculative. 


34  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

Whether  the  Moon  ever  revolved  on  its  axis  more  than 
once  in  each  revolution  around  the  Earth  is  not  known. 
If  it  ever  did,  its  process  of  formation  or  volcanic  action 
during  its  cooling  and  hardening  process  may  have 
changed  its  form  a  little,  thereby  shifting  the  cen- 
ter of  gravity  until  it  assumed  its  more  recent  or 
present  motions.  The  revolutions  of  the  Moon  on  its 
axis  are  claimed  by  some  to  be  absolutely  uniform.  Yet 
we  know  that  the  Moon  travels  faster  in  some  parts  of  its 
orbit  than  in  others.  When  near  perigee  it  often  travels 
from  quarter  to  quarter  in  a  little  more  than  six  and  a  half 
days ;  when  near  apogee  it  often  takes  nearly  eight  and 
one-quarter  days  to  go  from  quarter  to  quarter,  or  to  make 
one-fourth  of  one  revolution  on  its  axis.  Sometimes  an  ex- 
tremely slow  quarter  precedes  a  fast  one,  and  sometimes  a 
fast  one  precedes  a  slow  one.  If  it  were  revolving  on  its 
axis  at  the  slow  rate,  or  once  in  about  thirty-three  days, 
and  quickly  got  into  conditions  where  it  would  need  to  re- 
volve on  its  axis  once  in  about  twenty-six  days,  the  attrac- 
tion of  the  Earth  on  the  Moon  might  not  be  sufficient  to 
change  the  velocity  of  its  axial  rotation  so  suddenly,  and  it 
would  seem  to  pass  along  or  ahead  of  its  mean  place  and 
allow  us  to  see  a  little  of  the  farther  half  of  it.  Or,  if  its 
axial  rotation  occurred  once  in  about  twenty-six  days,  its 
momentum  might  revolve  it  a  little  beyond  its  mean  posi- 
tion, at  times  when  its  axial  velocity  would  be  reduced  to 
one  revolution  in  about  thirty-three  days.  In  each  case 
we  would  be  enabled  to  see  a  little  more  of  the  Moon,  first 
on  one  side  and  then  on  the  other,  than  when  in  its  mean 
position.  If  the  orbital  revolution  of  the  Moon  should 
change  from  its  present  time  to  either  twenty-six  or  thirty- 
three  days,  the  Earth's  attraction  would  evidently  change 
its  axial  rotation  accordingly. 

The  axis  of  rotation  of  the  Moon  is  inclined  about  one 
and  one-half  degrees  to  its  orbit,  which,  taken  in  connection 
with  the  inclination  of  its  orbit  to  the  ecliptic,  makes  it  ap- 
pear at  times  to  tip  forward  and  backward  about  thirteen 
degrees,  which  enables  us  to  look  a  little  over  its  North 
Pole,  and  when  in  opposite  positions  a  little  over  its  South 


THE    MOON.  35 

Pole.  If  the  Moon  is  observed  first  from  one  side  of  the 
Earth  and  then  from  the  other  at  proper  times,  a  little  more 
than  one-half  of  the  Moon  can  be  seen,  on  account  of  the 
Earth  being  so  much  larger  than  the  Moon  we  see'  a  little 
over  the  edge  of  it.  But,  if  viewing  the  Moon  from  any 
one  point,  not  taking  into  account  its  oscillating  move- 
ments, we  never  see  quite  one-half  of  it,  owing  to  the  lines 
of  vision  starting  from  one  point  and  not  being  able  to 
reach  over  to  an  imaginary  diameter  of  the  Moon,  as  placed 
or  located  at  right-angles  with  the  line  of  observation. 
These  several  apparently  oscillating  movements  of  the  Moon 
are  called  its  librations. 

When  we  take  into  consideration  the  immense  speed  at 
which  the  Earth  is  traveling  around  the  Sun,  the  several 
motions  of  the  Moon,  together  with  the  rapidity  with  which 
it  passes  from  one  position  to  another,  and  the  influence  of 
the  attraction  of  the  Earth  and  Sun,  also  the  throwing-off 
force  of  the  Sun,  etc.,  it  will  be  seen  how  difficult  it  is  to 
account  for  its  various  and  multiple  positions  without  the 
aid  of  apparatus  to  illustrate  them. 

The  conduct  of  the  Moon  in  going  once  around  in  its 
orbit,  when  carefully  noted  in  its  entire  circuit,  seems  to  ex- 
hibit more  positive  signs  of  the  throwing-off  force  of  the 
Earth  than  any  other  example  which  is  given  us  among  the 
planets.  If,  starting  with  the  full  moon,  we  find  it  outside 
the  Earth's  orbit,  and  in  a  position  relative  to  the  force  of 
the  Earth  (as  shown  in  diagram),  that  would  naturally 
cause  it  to  gain  on  the  Earth,  as  it  appears  to  be  continually 
driven  along  and  ahead  by  the  Earth's  force,  until  it  is  car- 
ried around  in  front  of,  or  in  advance  of  the  Earth,  where  it 
crosses  the  Earth's  orbit  at  the  beginning  of  the  fourth 
quarter,  and  is  still  driven  ahead  and  a  little  to  one  side, 
where  its  position  is  such  that  the  tangent  force  lines  from  the 
Earth  would  not  have  the  effect  of  sending  it  on  still  ahead 
of  the  Earth,  but  would  rather  appear  to  push  it  to  one  side 
and  to  partially  or  gradually  hold  it  back  and  to  bear  it 
away  until  the  Earth  passed  it  sufficiently  to  allow  it  to  be 
drawn  toward  the  Earth  by  attraction,  and  at  the  same  time 
press  it  behind,  or  in  the  rear  of  the  Earth,  by  the  Earth's 


36  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

throwing-off  force.  From  there  it  soon  gets  into  harmony 
with  the  direct  force  rays  of  the  Earth,  and  is  enabled  to 
gain  upon  and  to  pass  the  Earth  again  at  full  moon.  Ow- 
ing to  the  different  degrees  of  the  Earth's  force  that  the 
Moon  is  traveling  in,  the  points  of  apogee  and  perigee  var}^ 
considerably  in  the  Moon's  orbit.  Sometimes  the  Moon 
passes  from  one  point  to  the  other  in  about  twelve  days, 
while  in  the  following  or  preceding  year  and  in  the  corres- 
ponding Moon,  it  would  take  about  sixteen  days.  On  the 
average  the  Moon  is  thrown  a  little  further  round  at  each 
or  every  revolution,  causing  the  points  of  apogee  and  peri- 
gee to  advance  in  the  Moon's  orbit. 

To  this  same  force  may  be  assigned  the  principal  cause  for 
the  inclination  and  change  of  the  Moon's  orbit  as  shown  by 
its  nodes,  which  are  gradually  falling  back  probably  because 
it  is  not  thrown  quite  as  far  to  the  south  as  it  is  to  the 
north  of  the  Earth's  force,  and  it  gets  back  to  the  plane  of 
the  ecliptic  a  little  sooner  each  time,  which  action  would 
cause  the  retrograde  movement.  The  intervals  between  the 
nodes  are  much  more  uniform  than  between  the  apogee  and 
perigee.  According  to  M.  Ligner,  the  Austrian  meteorol- 
ogist, the  Moon  has  an  influence  on  a  magnetic  needle, 
which  appears  to  be  greatest  when  the  Moon  is  in  the  plane 
of  the  Earth's  equator,  and  also  greater  when  the  Moon 
is  south  than  when  it  is  north  of  the  ecliptic. 


Mars  is  also  shown,  in  Figures  II  and  IV,  as  the  fourth 
planet  from  the  Sun,  revolving  on  its  axis  and  around  the 
Sun  from  west  to  east.  Its  diameter  is  about  four  thousand 
two  hundred  miles.  Its  orbit  is  considerably  more  ellip- 
tical than  the  Earth's.  Its  mean  distance  from  the  Sun  is 
about  one  hundred  and  forty-one  million  miles.  Accord- 
ing to  observation  its  axial  rotation  is  twenty-four  hours 
thirty-seven  minutes  and  about  twenty-two  seconds.  About 
six  hundred  and  eighty-seven  days  are  required  for  one 
orbital  revolution.  Its  axial  equatorial  velocity  is  only 
about  five  hundred  and  thirty-six  miles  per  hour,  while  our 
Earth's  velocity  is  a  little  more  than  one  thousand.  There- 


MARS.  37 

fore  it  appears  that  the  equatorial  force  of  Mars  must  be 
much  less  than  that  of  our  Earth.  Mars  has  two  small  sat- 
ellites traveling  from  west  to  east,  and,  according  to  the 
more  recent  authors,  their  orbits  are  about  circular  and  lie 
nearly  in  line  with  the  planet's  equator.  Phobos,  or  the 
inner  satellite,  is  about  eleven  miles  in  diameter,  and  trav- 
els around  its  primary  at  an  average  distance  of  about  five 
thousand  eight  hundred  miles  in  seven  hours  and  nearlv 
forty  minutes,  thus  making  a  little  more  than  three  revo- 
lutions around  the  planet  while  the  planet  rotates  once  on 
its  axis.  This  would  cause  the  satellite  to  rise  in  the  west 
and  set  in  the  east,  if  observed  from  Mars,  and  this  would 
make  it  appear  to  meet  the  stars,  the  Sun  and  the  other  sat- 
ellite. Its  orbital  velocity  is  about  eighty  miles  per  min- 
ute, not  taking  into  account  the  distance  that  it  travels 
along  the  orbit  of  its  primary. 

The  outer  satellite,  Deimos,  is  about  eight  miles  in  diam- 
eter, and  about  fourteen  thousand  miles  from  the  planet. 
It  makes  one  orbital  revolution  in  thirty  hours  and  about 
eighteen  minutes.  Its  orbital  velocity  is  about  forty-seven 
and  a  half  miles  per  minute,  while  our  own  Moon  only  appears 
to  be  traveling  at  the  rate  of  about  thirty-five  miles  per 
minute.  If  the  paths  of  Phobos  and  Deimos  were  shown 
in  diagram  along  the  orbit  of  Mars,  they  would  be  seen 
crossing  and  recrossing  it  in  a  similar  manner  to  that  of  our 
Earth's  satellite,  except  that  the  intervals  of  crossing  would 
appear  nearer  together  and  a  little  more  scolloped.  As 
Mars  revolves  on  its  axis  once  in  about  twenty-four  hours, 
any  given  meridian  on  its  surface  would  gain  on  Deimos  so 
slowly,  that  it  would  appear  to  rise  very  slowly  in  the  east, 
and  after  a  little  more  than  five  days  would  appear,  to  set 
slowly  in  the  west. 

Figures  1 1  and  IV  also  represent  Mars  as  being  subject  to  the 
same  influence  and  controlled  in  like  manner  by  the  same 
forces  as  the  planets  between  it  and  the  Sun.  The  thro  wing- 
off  force  is  well  illustrated  by  Mars  and  its  satellites.  As 
Mars  has  an  equatorial  axial  velocity  of  only  about  five 
hundred  and  forty  miles  per  hour,  the  force  that  it  devel- 
ops by  its  rotation  must  be  proportionately  less  than  those 

314018 


38  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

which  have  a  greater  equatorial  velocity.  This  is  shown 
by  the  near  approach  of  the  satellites  to  the  planet,  it  ap- 
pearing scarcely  able  to  keep  the  inner  satellite  from  join- 
ing it.  Although  this  force  is  apparently  small,  yet  it  seems 
to  be  clearly  shown  to  be  in  operation  when  the  satellite 
Phobos  is  crossing  the  planet's  orbit  only  five  thousand 
eight  hundred  miles  in  front,  or  in  the  advance  of,  its  pri- 
mary, for  it  must  be  speedily  carried  or  urged  along  and  to 
one  side,  for  it  takes  Mars  only  about  six  minutes  to  travel 
in  its  orbit  the  distance  that  Phobos  is  from  it.  After  cross- 
ing the  orbit  in  front  of  the  planet  the  satellite  gradually 
slackens  its  speed  as  Mars  passes  along,  and  then  recrosses 
the  orbit  in  the  rear  of  the  planet,  then  gains  on  and  over- 
takes the  planet  in  relation  to  the  Sun  at  a  point  corres- 
ponding to  our  full  moon,  and  from  there  it  continues  to 
gain  until  it  arrives  at  the  orbit  in  front  of  the  planet  again, 
thus  making  an  entire  revolution  in  seven  hours  and  nearly 
forty  minutes.  The  outer  satellite  is  being  operated  upon 
in  the  same  manner,  although  its  movements  are  not  so 
rapid. 

If  we  should  presume  that  there  is  a  gaseous,  electric,  or 
other  influences  surrounding  the  planets  Mercury,  Venus, 
the  Earth  and  Mars,  and  which,  if  extended  far  enough 
from  their  surfaces  so  that  when  the  Sun's  force  would  act 
upon  them  at  a  distance,  that  would  roll  them,  together 
with  the  gaseous  envelope,  along  in  their  orbits  instead  of 
swinging  them,  they  would  require  gaseous  depths  from  the 
planets  about  as  follows,  in  order  that  they  should  roll 
around  the  number  of  times  that  they  are  said  to  rotate  on 
their  axes,  while  going  once  around  the  Sun :  Mercury, 
about  409,000  miles;  Venus,  about  270,000  miles;  the  Earth, 
about  250,000  miles,  and  Mars,  about  209,000  miles.  These 
decreasing  depths  that  would  appear  to  be  required  with 
each  planet,  correspond  to  the  decreasing  orbital  velocity  as 
regards  the  distance  of  each  respective  planet  from  the  Sun. 

ASTEROIDS. 

All  of  the  Asteroids  so  far  discovered,  and  which  now 
number  about  two  hundred  and  seventv,  revolve  in  orbits 


ASTEROIDS. JUPITER.  39 

between  the  orbits  of  the  planets  Mars  and  Jupiter,  and  ap- 
pear to  obey  the  same  general  law  as  regards  their  move- 
ments from  west  to  east  around  the  Sun,  as  well  as  in  the 
ellipticity  of  their  orbits.  Of  their  axial  rotations  nothing 
is  known.  Only  a  very  few  of  them  are  ever  seen  without 
the  aid  of  instruments,  and  not  much  interest  is  attached 
to  their  discovery,  or  even  to  their  existence,  except  to  the 
astronomical  student.  Their  names,  times  of  orbital  revolu- 
tion, many  of  their  diameters,  inclination  of  their  orbits  to 
the  ecliptic,  etc.,  are  tabled  in  mostof  the  text-books  so  com- 
pletely that  a  reference  to  their  movements  as  being  in  har- 
mony with  the  general  law  or  force,  as  previously  de- 
scribed and  illustrated,  is  deemed  sufficient. 


Jupiter  is  shown  in  Figure  IV  as  the  fifth  planet  from 
the  Sun,  and  controlled  by  the  same  force  and  influence  as 
the  planetary  bodies  previously  described.  It  is  the  largest 
planet  of  the  solar  system.  Its  equatorial  diameter  is 
claimed  by  some  authors  to  be  about  eighty-five  thousand 
miles,  and  by  some  as  great  as  ninety  thousand  miles.  The 
polar  diameter  is  estimated  to  be  about  fifty-five  hundred 
miles  less.  After  many  careful  observations,  authors  gen- 
erally agree  that  it  rotates  on  its  axis  once  in  nine  hours 
and  about  fifty-five  minutes.  It  travels  around  the  Sun  in 
about  four  thousand  three  hundred  and  thirty-two  and 
one-half  days,  at  a  mean  distance  of  about  four  hundred 
and  eighty-three  million  miles,  in  an  orbit  considerably 
elliptical  and  inclined  one  degree  and  about  eighteen  min- 
utes to  the  ecliptic.  Its  axis  is  inclined  only  about  three 
degrees  to  its  orbit ;  therefore  there  would  be  scarcely  any 
change  in  its  seasons.  The  excess  of  the  equatorial  over 
the  polar  diameter  is,  without  doubt,  caused  by  its  rapid 
rotation  on  its  axis,  together  with  the  tidal  action  and  effect 
produced  by  its  moons.  Belts  are  seen  to  extend  across  the 
planet  parallel  to  its  equator,  and  which  are  constantly 
changing,  sometimes  increasing  or  decreasing  in  number 
and  size,  and  sometimes  appearing  |to  change  color.  Spots 
frequently  appear  on  its  surface,  and  by  them  the  time  of 


40  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

its  axial  rotation  has  been  determined.  The  spots  near  the 
equator  have  the  same  peculiarity  of  traveling  faster  than 
those  farther  from  it,  as  they  do  on  the  Sun,  which  is  prob- 
ably owing  to  the  tidal  effect  of  the  moons,  as  they  are  all  nearly 
in  line  with  the  plane  of  the  planet's  equator.  If  the  influ- 
ence of  the  moons  of  Jupiter  produce  an  effect  on  its  sur- 
face similar  to  our  own  satellite  on  the  Earth's  surface,  the 
movable  substances  near  the  equator  of  Jupiter  would  be 
correspondingly  changed  in  their  positions,  while  the  spots 
farther  from  it  might  be  moved  along  a  little  in  proportion 
to  the  tidal  effect,  which  would  imply  that  the  spots  which 
are  traveling  the  slowest  are  traveling  somewhat  faster 
than  the  body  of  the  planet  really  revolves.  The  fact  of 
there  being  a  difference  in  the  speed  of  the  spots  on  the 
planet's  surface  is  evident  that  the  planet  itself  is  either 
traveling  faster  than  the  fastest  spots,  and  causing  them  to 
follow,  according  to  the  centrifugal  effect  of  the  planet,  or 
slower  than  the  slowest,  and  by  its  greater  throwing-off 
force  near  the  equator,  in  connection  with  its  moons,  is  urg- 
ing the  spots  along  at  that  part  of  its  surface  more  rapidly. 
It  seems  very  much  at  variance  with  the  law  of  mechanics 
that  there  should  be  a  medium  speed  between  the  times  of 
the  rotation  of  the  spots  at  which  the  motive  power  is  mov- 
ing. 

As  all  of  the  planets  lie  nearly  in  the  Sun's  equatorial 
plane,  or  in  nearly  the  same  relation  to  the  Sun  as  the 
moons  of  Jupiter  do  to  it,  so  it  would  appear  that  the  same 
cause  or  principle  which  would  advance  a  spot  on  one 
could  also  be  claimed  to  advance  it  on  the  other. 

The  Sun's  force  seems  to  be  applied  differently  to  the 
planets  which  revolve  in  their  orbits  outside  of,  or  beyond, 
the  asteroids,  while  it  seems  to  be  controlling  the  four  inner 
planets  by  acting  upon  the  gaseous  fluid  or  influence  which 
surrounds  them  at  various  distances  from  them.  The  force 
appears  to  be  applied  almost,  if  not  quite  directly,  to  the 
surfaces  of  the  four  which  are  beyond  the  asteroids.  For, 
if  we  presume  Jupiter  to  be  rolled  around  in  its  orbit,  with 
no  allowance  to  be  made  for  its  being  in  an  elastic  medium, 
we  would  have  the  number  of  rotations  that  it  would  make 


MOONS   OP   JUPITER.  41 

in  one  orbital  revolution  by  dividing  its  orbital  distance  by 
the  circumference  of  the  planet.  Then  divide  the  time  of 
one  orbital  revolution  by  the  number  of  rotations  obtained, 
and  we  shall  have  the  time  for  each  rotation  on  its  axis. 
The  result  thus  obtained  varies  from  nine  hours  and  about 
nineteen  minutes  to  nine  hours  and  about  forty-two  min- 
utes, according  to  the  diameters  and  distances  given  by  dif- 
ferent authors.  Diameters  given  by  one  author  and  dis- 
tances given  by  another  could  be  selected,  which  would  give 
results  that  would  be  quite  near  to  the  time  given  by  those 
who  have  made  careful  observations.  Jupiter's  orbital  ve- 
locity is  about  five  hundred  miles  per  minute,  and  its  equa- 
torial axial  velocity  is  about  for  hundred  and  sixty  miles 
per  minute. 

MOONS   OF   JUPITER. 

Jupiter  has  four  moons  traveling  around  in  orbits  from 
west  to  east,  and  at  distances  from  the  primaries  about  as 
follows,  respectively :  Two  hundred  and  sixty-seven  thou- 
sand miles;  425,000  miles;  687,000  miles,  and  1,193,000 
miles,  and  whose  orbital  revolutions  occur  in  one  day 
eighteen  hours  and  about  twenty  minutes ;  three  days  thir- 
teen hours ;  seven  days  three  hours  and  forty  minutes,  and 
from  sixteen  to  eighteen  days  for  the  fourth,  or  farthest  one. 
Their  orbital  velocities  also  decrease  as  their  distances  in- 
crease, from  about  seven  hundred  miles  per  minute  for  the 
nearest,  to  about  three  hundred  and  ten  miles  per  minute" 
for  the  farthest.  All  of  the  moons  cross  and  recross  the 
orbits  of  Jupiter  in  the  same  manner  as  those  of  Mars  and 
our  own,  except  that  if  illustrated  their  paths  would  appear 
much  more  scolloped  and  the  crossings  much  nearer  in  pro- 
portion, while  the  inner  one  must  very  nearly  make  a  loop 
in  its  orbit  when  passing  between  Jupiter  and  the  Sun. 

The  positions,  etc.,  of  all  of  the  moons  of  Jupiter  seem 
to  confirm  the  theory  in  regard  to  the  manner  and  direc- 
tion of  the.  repelling  forces,  as  heretofore  designated.  The 
orbits  of  the  moons  of  Jupiter  correspond  very  nearly  to 
the  orbit  of  Venus  in  relation  to  the  Sun,  in  that  they  are 
all  nearly  in  line  with  the  equatorial  plane,  and  all  nearly 
circular. 


42  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

The  inclination  of  a  planet's  orbit  to  the  Sun's  equa- 
torial plane,  or  force  line,  does  not  always  determine  the 
ellipticity  of  the  planet's  orbit,  because  the  planet  may 
be  traveling  so  far  away  from  the  Sun  that  a  less  angle 
would  carry  it  farther  to  one  side  of  the  Sun's  force  line 
than  planets  which  are  nearer  with  a  greater  orbital  incli- 
nation to  the  Sun's  force. 

SATURN. 

Saturn  is  also  shown  in  Figure  IV.  It  is  the  sixth  prin- 
cipal planet  in  distance  from  the  Sun,  and  the  farthest  one 
of  our  solar  system  which  was  known  to  the  ancients.  The 
author  has  never  seen  any  evidence  of  any  knowledge  by 
them  of  its  ringed  appearance.  Saturn  is  the  next  largest 
in  size  of  all  the  planets  belonging  to  the  solar  system,  it 
being  from  about  seventy  thousand  to  seventy-four  thousand 
miles  in  diameter,  according  to  different  authors.  Its  mean 
distance  from  the  Sun  is  variously  stated  at  from  eight 
hundred  and  seventy-two  million  miles  to  nearly  eight 
hundred  and  eighty-eight  million  miles.  Its  poles  are 
inclined  about  twenty-eight  degrees  to  the  ecliptic,  and  late 
authors  give  ten  hours  and  about  fourteen  minutes  as  its 
axial  rotation,  and  about  twenty-nine  and  a  half  years  as 
its  orbital  revolution.  Its  orbit  is  considerably  elliptical, 
and  but  little  inclined  to  the  ecliptic.  Changeable  bands 
or  belts  appear  to  surround  the  planet,  parallel  to  its  equa- 
tor, similar  to  those  of  Jupiter,  and  spots  have  also  occa- 
sionally been  seen  on  its  surface,  by  which  its  time  of  rota- 
tion has  been  determined.  Although  Saturn  does  not 
revolve  as  fast  as  Jupiter,  yet  its  equatorial  diameter  is  sup- 
posed to  be  greater  in  proportion ;  but  it  corresponds  to  the 
almost  continual  tidal  effect  which  its  more  numerous  and 
oftener-appearing  moons  would  produce,  although  there  is 
not  much  difference  between  their  combined  bulk  and 
those  of  Jupiter. 

MOONS   OF   SATURN. 

Saturn  has  eight  moons,  revolving  at  distances  varying 
from  nearly  one  hundred  and  twenty-one  thousand  miles 
to  nearly  two  million  five  hundred  thousand  miles  from  the 


MOONS   OF   SATURN. — RINGS   OF   SATURN.  43 

primary,  and  with  a  decreasing  velocity  respectively  from 
about  five  hundred  and  sixty  miles  to  about  one  hundred 
and  twenty-seven  miles  per  minute,  not  considering  the 
orbital  velocity  of  Saturn.  Nearly  all  of  their  orbits  lie 
close  to  the  line  of  the  equator  of  Saturn,  which  circum- 
stance would  indicate  that  their  orbits  are  nearly  circular, 
or  similar  to  the  orbits  of  the  moons  of  Jupiter  and  the  orb  it 
of  the  planet  Venus.  If  a  wheel  were  rolled  along  the  side 
of  a  vertical  plane  surface  with  points  fixed  at  various  dis- 
tances between  the  center  and  the  rim  of  the  wheel  for 
marking  on  this  surface,  the  lines  produced  would  some- 
what represent  the  paths  of  the  satellites  along  the  orbits  of 
their  primaries.  One  placed  at  a  point  about  three-fourths 
the  distance  from  the  rim  to  the  center  of  the  wheel,  would 
nearly  represent  the  path  of  our  own  Moon  along  the  orbit 
of  the  Earth,  while  those  nearer  the  rim  would  better  rep- 
resent the  paths  of  the  satellites  of  Jupiter  and  Saturn.  The 
straight  line  caused  by  the  axis  of  the  wheel  would  repre- 
sent the  orbit  of  the  planets.  The  inner  satellite  of  Saturn 
nearly,  if  not  quite,  makes  a  small  loop  in  its  path  while 
passing  between  its  primary  and  the  Sun  at  each  revolution 
around  the  planet.  If  the  orbital  distance  of  Saturn  be 
divided  by  the  planet's  circumference  to  obtain  the  number 
of  rotations  in  going  once  around  the  Sun,  and  the  time  of 
one  orbital  revolution  be  divided  by  the  number  of  rotations 
thus  obtained,  we  shall  have  from  ten  hours  and  about 
thirteen  minutes  to  ten  hours  and  about  thirty-eight  min- 
utes as  the  time  for  Saturn  to  revolve  once  on  its  axis,  ac- 
cording to  diameters,  distances  and  times  given  by  several  of 
the  latest  authors,  extreme  results  either  way  being  omitted. 

RINGS   OF    SATURN. 

Saturn  is  surrounded  with  several  rings  of  a  material 
which  seems  to  reflect  the  light  of  the  Sun  as  it  shines  upon 
them.  All  of  the  rings  lie  in  the  equatorial  plane  of  the 
planet.  The  outer  diameter  of  the  outer  ring  is  about  one 
hundred  and  sixty-six  thousand  miles.  The  outer  rings 
appear  very  thin  when  the  edge  is  presented  to  the  Earth, 
while  near  the  planet  they  seem  to  be  a  little  thicker. 


44  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

Some  claim  to  have  observed  spots  on  the  rings  by  which 
they  presume  the  time  of  their  rotation  to  be  but  little  less 
than  that  of  the  planet.  The  manner  in  which  the  rings 
are  suspended  at  different  distances  from  the  planet  indi- 
cates that  they  are  of  different  substances  and  of  different 
degrees  of  specific  gravity.  This  also  shows  the  force  of 
the  planet  acting  through  one  substance  and  upon  another 
beyond.  The  rings  of  Saturn  furnish  us  the  best  ocular 
demonstration,  in  the  solar  system,  of  the  throwing-off  force 
of  the  revolving  planetary  bodies.  Although  the  rest  of 
the  planets  may  not  gather  from  space  or  throw  off  from 
themselves  a  substance  that  reflects  or  emits  light,  yet  the 
action  or  force  which  produced  the  rings  and  still  continues 
to  hold  the  substances  of  which  they  are  composed  sus- 
pended in  the  position  where  the  operation  of  the  law  placed 
them,  must  have  been  developed  long  before  the  rings  were 
formed,  or  at  the  times  when  the  planets  commenced  to  ro- 
tate on  their  axes. 

All  substances  or  influences  before  being  thrown  off  from 
a  revolving  body  or  sphere  by  centrifugal  force  seek  that 
part  near  the  equator,  and  which  is  farthest  from  its  axis, 
and  where  the  axial  velocity  is  greatest,  before  being 
thrown  off,  and,  of  course,  cannot  be  returned  by  attraction 
to  the  body  at  that  part  of  its  surface ;  but  after  the  centri- 
fugal force  of  the  body  has  ceased  to  effect  the  substance  or 
influence  that  is  thrown  off,  then  should  it  return  to 
the  planet  by  the  planet's  attraction,  it  must  do  so  on  one 
or  the  other  side  of  this  force  which  sent  it  away,  and  which 
is  constantly  kept  up  by  the  rotation  of  the  revolving  planet. 

URANUS. 

Uranus  is  the  seventh  principal  planet  from  the  Sun,  and 
is  so  far  away  that  it  is  seldom  seen  with  the  naked  eye. 
Its  diameter  is  about  thirty-three  thousand  miles.  It  trav- 
els from  west  to  east  around  the  Sun  in  an  elliptical  orbit 
which  lies  about  in  line  with  the  Earth's,  and  at  an  average 
distance  of  about  one  billion  seven  hundred  and  eighty -five 
million  miles  from  the  Sun.  Its  orbital  velocity  is  about  two 
hundred  and  sixty  miles  per  minute,  and  it  makes  one  revo- 


UKANUS. — NEPTUNE.  45 

lution  around  the  Sun  in  about  eighty-four  years.  The  time 
of  its  axial  rotation  is  unknown.  Some  of  the  later  writers 
have  placed  it  at  about  seven  hours,  and  some  from  nine 
and  a  half  to  ten  hours.  If  calculated  by  dividing  its  orbital 
distance  by  the  planet's  circumference,  etc.,  in  the  same 
manner  as  Jupiter  and  Saturn,  we  shall  have  about  seven 
hours  as  the  time  required  for  one  axial  rotation. 

NEPTUNE. 

Neptune  is  the  eighth  and  farthest  planet  from  the  Sun 
yet  discovered.  It  is  so  far  away  that  it  is  never  seen  with 
the  naked  eye.  Its  diameter  is  about  thirty-seven  thou- 
sand miles.  It  travels  from  west  to  east  around  the  Sun,  at 
a  mean  distance  of  about  two  billion  eight  hundred  million 
miles,  once  in  about  one  hundred  and  sixty-four  years,  with 
an  orbital  velocity  of  about  two  hundred  miles  per  minute. 
Its  orbit  is  elliptical,  and  inclined  but  little  to  the  ecliptic. 
The  author  has  seen  no  estimates  of  the  time  of  its  axial  ro- 
tation. About  nine  and  a  half  hours  would  be  the  result 
if  calculated  by  its  circumference  and  orbital  distance,  etc., 
as  with  Jupiter,  Saturn  and  Uranus. 

MOONS    OF    URANUS    AND    NEPTUNE. 

Uranus  has  four  Moons  and  Neptune  one.  They  are  said 
to  move  in  orbits  greatly  inclined  to  the  ecliptic,  and  in  a 
retrograde  manner,  or  from  east  to  west,  around  their  pri- 
maries, motions  which  are  contrary  to  all  the  rest  of  the 
planetary  bodies  of  our  solar  system,  the  cause  for  which 
will  probably  be  explained  as  science  advances. 

The  points  of  intersection  of  the  orbits  of  the  planets 
with  the  plane  of  the  Sun's  equator  do  not  occur  in  the 
same  place  at  every  revolution  of  the  planet  in  its  orbit. 
They  either  advance  or  fall  back  on  the  Sun's  equatorial 
plane  similar  to  the  Earth's  satellite  in  regard  to  its  nodes 
or  apsides.  Some  of  the  planets  vary  more  than  others, 
but  the  point  of  intersection  with  the  Sun's  equatorial 
plane  is  according  to  the  extent  that  the  Sun's  force  sends 
them  away  after  leaving  their  perihelion. 


46  MECHANICS   APPLIED    TO   THE   SOLAR   SYSTEM. 


MKAN    DISTANCES. 

The  mean  distances  of  the  planets  from  the  Sun  are  ob- 
tained by  adding  the  perihelion  and  aphelion  distances 
together  and  then  assuming  one-half  of  the  amount  thus 
obtained  to  be  the  average  distance  of  the  planet  from  the 
Sun.  (See  Mean  Distance,  Lockyer's  Index.)  The  point 
thus  obtained  is  one  which  corresponds  to  the  central  point 
of  an  ellipse,  a  position  that  the  Sun  never  occupies  in  rela- 
tion to  any  of  the  planets.  It  is  always  nearest  the  peri- 
helion side  of  the  orbit.  The  position  thus  occupied  by  the 
Sun  in  relation  to  the  Earth  is  best  seen  at  the  time  of  the 
equinoxes.  If  an  imaginary  line  were  drawn  across  the 
Earth's  orbit  at  those  times  and  to  those  points,  it  would 
intercept  the  Sun,  but  would  not  be  far  enough  from  the 
Earth's  perihelion  to  reach  the  central  point  of  the  long 
diameter  of  the  Earth's  orbit.  Aline  from  the  perihelion 
to  the  aphelion  points  of  a  planet's  orbit  shows  nearly  the 
line  of  the  long  diameter  of  the  orbit,  but  the  line  from 
equinox  to  equinox  does  not  show  the  short  diameter  of 
the  elliptical  orbit,  as  the  line  which  intercepts  the  equi- 
noxes is  always  nearer  the  perihelion  than  the  line  of  the 
short  diameter.  In  mechanics,  the  sum  of  one  quarter  of 
the  short  diameter  and  one  quarter  of  the  long  diameter  of 
an  ellipse  added  together,  gives  about  one-half  of  the  aver- 
age diameter  of  an  ellipse,  and  one-half  of  the  sum  of  two 
unequal  distances,  which  make  a  diameter,  gives  us  only 
the  radius  of  a  true  circle.  The  mean  distances  of  the 
planets  from  the  Sun,  as  given  by  various  authors,  is  prob- 
ably not  far  from  being  correct,  for  the  orbits  of  the  planets 
are  probably  nearer  circular  than  they  are  generally  stated 
to  be.  If  we  presume  the  orbit  of  Venus  to  be  a  true  circle, 
with  the  Sun  placed  far  enough  to  one  side  of  the  center  of 
the  orbit  to  indicate  the  ellipticity,  as  claimed  by  authors, 
or  so  that  Venus  is  nine  hundred  thousand  miles  nearer 
the  Sun  at  perihelion  than  at  aphelion,  one  side  of  the  Sun 
would  then  be  within  twenty  thousand  miles  of  the  center 
of  the  orbit.  It  is  obvious  that  if  we  presume  the  circle  to 
then  be  flattened  so  that  the  short  diameter  will  be  nine 


MEAN    DISTANCES. COMETS. 


47 


hundred  thousand  miles  less  than  the  long  diameter,  the 
entire  half  of  the  orbit  on  the  perihelion  side  of  the  Sun 
would  be  about  the  same  distance  from  the  Sun,  conditions 
which  are  entirely  unnatural,  and  which  no  astronomer 
admits. 

The  Earth  is  traveling  around  in  its  orbit,  with  the  Sun 
not  two  million  miles  distant  from  the  center  of  the  Earth's 
orbit.  If  we  should  presume  the  orbit  to  be  a  true  circle 
with  the  Sun  at  that  distance  from  the  center,  it  seems  clear 
that  the  orbit  would  admit  of  but  very  little  ellipticity,  else 
the  Earth  could  not  increase  its  distance  much  from  the 
Sun  between  the  time  of  its  perihelion  and  its  arrival  at  its 
equinox.  The  following  table  is  deduced  from  the  table  of 
distances,  etc.,  of  some  of  the  latest  calculations: 

TABLE  OF  THE  APPROXIMATE  DIAMETERS  OP  THE  SUN  AND  PRINCI- 
PAL PLANETS,  SOLAR  DISTANCES,  ETC. 


MEAN  DI- 
AMETER IN 
MILES. 

MEAN  SOLAR 
DISTANCE 
IN  MILES. 

ORBITAL 
REVO- 
LUTIONS. 

ORBITAL  VE- 
LOCITY PER 
MINUTE. 

AXIAL  ROTA- 
TION.*!'" 
SjBS'ACE. 

EQUATORIAL 
AXIAL  VEL. 
PEB  MIN. 

Sun  

866,000 

25d.   Oh.  Om.  Os, 

Ab't  76  miles 

Mercury 

3,000 

35,500,000 

88  days. 

1,700  miles. 

Od.  24h.   5m.  Os. 

"     7      " 

Venus.  .  . 

7,750 

67,000,000 

224|   •• 

1,300      " 

Od.  23h.  20m.  Os. 

<•    17J    » 

Earth... 

7,918 

93,000,000 

365J    • 

1,110      " 

Od.  23h.  56m.  4s. 

..    17      .. 

Mars.... 

4,200 

141,000,000 

687 

960      " 

Od.  24h.  37m.  +8. 

"     9      •• 

•Jupiter.. 

88,000 

483,000,000 

4.332J 

500      " 

Od.   9h.55m.  Os. 

"  460      " 

Saturn  .  . 

72,000 

885,000,000 

29iyrs. 

360      " 

Od.  lOh.  14m.  Os. 

•<  368      " 

Uranus.. 

33,000     1,785,000,000 

84     " 

260       • 

About?  h. 

"  242     " 

Neptune. 

37,000     2,800,000,000 

164      " 

200      " 

About  9Jh. 

••  204      " 

COMETS. 

The  supposed  orbits  of  some  of  the  most  noted  comets  are 
also  shown  in  Figure  IV.  The  application  of  the  same  law 
to  the  comets  as  to  the  planets  is  shown  by  the  radiating 
force  lines.  It  is  well  known  to  astronomers  that  the  tails 
of  comets  are  often  not  formed  until  sometime  after  the  dis- 
covery of  the  comets,  and  also  that  the  tails  extend  in  a  line 
from  the  comets  on  the  opposite  side  of  them  from  the  Sun, 
also  that  the  comets  approach  the  Sun  from  the  space  at 


48  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

either  side  of  the  plane  of  the  orbits  of  the  planets,  and  not 
from  that  region  of  space  near  the  Sun's  equatorial  plane  or 
where  the  Sun's  force  is  greatest,  as  shown  in  the  sec- 
tional edge-view  of  a  part  of  the  solar  system  in  Figure  II. 
Figure  IV  also  shows  the  comets  approaching  and  receding 
from  the  Sun.  If  approaching  from  either  side,  they  may 
be  under  the  radiating  influence  of  the  Sun  sufficiently  to 
form  the  tail  of  the  comet  while  at  the  same  time  the  force 
of  the  Sun  may  not  be  strong  enough  at  the  side  or  in  the 
region  of  the  comet  to  throw  it  away,  so  they  approach 
nearer  and  nearer  until  drawn  sufficiently  into  the  current 
to  be  thrown  away  again.  In  this  manner,  they  make  their 
varying  and  elliptical  orbits  as  shown,  the  ellipticity  of 
their  orbits  probably  depending,  to  a  great  extent,  on  their 
composition  and  the  extent  to  which  they  are  drawn  into 
the  Sun's  force. 

The  curvature  of  the  tail  of  the  comet  is  shown  as  being 
caused  by  the  force  of  the  Sun  carrying  particles  of  the 
cometary  matter  or  substance  off  in  the  directions  of  the 
Sun's  force  lines,  which  after  a  time  are  disseminated,  while 
others  are  continually  making  their  appearance  as  the 
comet  passes  along  in  its  orbit. 

The  great  comets  that  came  in  1881  and  1882  appeared 
so  suddenly  and  unexpectedly  that  they  were  not  seen  by 
many  until  the  maxima  of  their  tails  were  nearly  reached, 
thus  showing  that  they  entered  the  radiating  force  of  the 
Sun  in  a  short  period  of  time,  which  could  be  done  only 
from  the  side  of  this  force  where  they  would  be  affected  but 
little  until  when  drawn  into  the  force  they  quickly  appeared 
with  luminous  tails,  caused  by  contact  with  the  Sun's  repel- 
ling force  in  the  manner  shown  and  as  described.  The  tails 
of  comets  may  not  always  be  seen  as  formed  by  the  Sun's 
force  acting  upon  them  in  straight  lines,  for  they  are  not 
seen  in  the  direct  and  full  force  rays  of  the  Sun,  but  more 
or  less  to  one  or  the  other  side  where  the  force  is  weaker 
and  where  it  seems  to  be  falling  out  of  or  leaving  the  main 
current  in  irregular  lines. 

Comets  are  sometimes  known  to  approach  and  to  travel 
around  the  Sun  in  an  opposite  direction  from  which  the 


COMETS.  49 

planets  are  traveling  in  their  orbits.  Nearly  all  of  the 
comets  having  periods  of  return  of  about  one  hundred  years 
travel  around  the  Sun  in  the  same  general  direction  as  the 
planets,  or  from  west  to  east.  The  comets  which  do 
appear  more  regularly  and  which  have  the  same  general 
direction  as  the  planets,  might  be  presumed  to  have  a 
greater  specific  gravity  than  those  which  have  longer 
periods  of  return,  or  it  may  be  that  the  direction  or  angle  at 
which  they  approach  the  Sun  is  so  small  that  the  momen- 
tum which  the  comets  have  gained  by  the  attraction  of  the 
Sun  would  not  be  sufficient  to  cause  them  to  enter  far 
enough  into  the  Sun's  force,  at  the  time  of  their  supposed 
regular  visitations,  to  materially  change  the  orbit  of  the 
comets  and  their  time  of  return.  It  also  seems  but  natu- 
ral that  a  comet  which  has  been  returning  quite  regularly 
might,  for  some  reason,  approach  the  Sun  at  a  greater  angle 
on  some  occasions  than  on  others  and  by  its  momentum, 
gained  while  returning,  be  drawn  further  into  the  Sun's 
force  than  at  other  times  and  then  be  thrown  correspond- 
ingly farther  away,  which  would  delay  its  next  return  to  the 
Sun.  Some  of  the  comets  seem  to  keep  in  tolerably  well- 
defined  and  regular  orbits,  while  some  few  which  are 
claimed  to  not  return  are  said  to  have  orbits  as  described 
by  the  hyperbola.  It  seems  in  harmony  with  this  law,  if 
the  direction  which  the  comet  shall  have  already  attained  or 
acquired  should  lead  it  into  the  Sun's  force  more  and  more 
as  it  is  receding  from  the  Sun,  that  the  comet  would  assume 
a  more  and  more  direct  line  from  the  Sun,  and  would 
continue  in  line  with  the  force  until  the  force  became  spent 
in  space,  when  the  comet  would  cease  to  go  farther,  and  from 
that  point  might  return  to  the  Sun  again  from  either  side 
of  the  stream  of  force  which  sent  it  away.  It  has  been 
clearly  seen  that  some  comets  diminish  in  size  as  they 
approach  and  recede  from  the  Sun  until  they  are  lost  from 
view,  and  then  on  their  return  they  seem  to  have  increased 
in  size  again,  only  to  be  again  reduced  as  they  approach  and 
depart  from  the  Sun,  conditions  which  indicate  that  the 
substance  which  the  comet  attracted  to  itself  while  absent 
is  not  so  dense  that  the  Sun's  force  cannot  overcome  the 


50  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

attraction  of  the  nucleus  of  the  comet  for  the  particles  or 
substance  which  surround  it  and  of  which  the  body  of  the 
comet  may  be  composed.  As  these  particles  are  carried  off, 
they  usually  appear  luminous  and  form  the  tail  of  the 
comet,  as  previously  described. 

As  the  planets  have  attracted  to  themselves  different  sub- 
stances from  the  region  of  space  through  which  they  travel, 
so  it  would  follow  that  a  comet  while  absent  would  not 
necessarily  attract  or  take  up  the  substances  of  which  it  is 
composed  every  time  alike,  but  would  absorb  such  sub- 
stances as  it  passed  near  enough  to  attract  to  itself,  and 
when  reappearing  it  might  be  seen  with  the  same  nucleus 
as  before,  but  would  show  a  somewhat  different  composition 
than  it  did  on  its  preceding  visit.  If  a  comet  is  small  and 
lacks  density  it  may  be  entirely  worn  away  and  so  carried 
off  into  space  by  the  Sun's  force  rays,  under  which  circum- 
stances its  identity  must  forever  disappear,  while  the  sub- 
stance of  which  it  was  composed  might  be  absorbed  in  part 
by  other  comets,  if  not  by  planetary  bodies. 

The  tails  of  the  comets  are  sometimes  formed  at  immense 
velocities,  which,  it  seems,  could  not  exceed  the  combined 
velocities  of  the  comet  going  toward  the  Sun  in  one  direc- 
tion and  of  the  particles  or  substances  which  are  carried  in 
the  opposite  direction  by  the  Sun's  force.  The  speed  with 
which  the  particles  are  carried  away  from  the  comet  fur- 
nishes the  best  means  of  telling  the  speed  of,  and  the  dis- 
tance from,  the  Sun's  surface,  at  which  the  Sun's  force  is 
thrown  off. 

It  would  seem,  from  the  easy  manner  in  which  the  Sun 
appears  to  control  the  comets  and  the  power  that  it  has  over 
them,  that  they  could  never  come  as  a  body  in  contact  with 
any  of  the  planets,  because  the  Sun's  force  is  so  great  in  the 
region  of  the  planets  that  a  comet  would  be  thrown  back 
into  the  space  beyond  again,  if  it  were  to  approach  the  Sun 
from  that  direction ;  and  again,  the  force  which  is  developed 
by  the  rotation  of  the  principal  planets  on  their  axes  and 
which  keeps  their  satellites  in  their  orbits,  would  be  suffi- 
cient to  repel  a  comet  if  approaching  from  near  the  plan- 
et's equatorial  plane.  If  approaching  from  either  side  of 


COMETS.  51 

this  force,  the  greatest  attraction  would  be  that  of  the  Sun, 
to  which  it  would  be  drawn  as  near  as  the  Sun's  throwing- 
off  force  would  allow. 

As  the  Sun  is  traveling  through  space,  it  might  attract  to 
itself  a  cometary  body  or  substance  from  the  deep,  and  one 
with  which  it  never  came  in  contact  before,  and  then  throw 
it  off  to  the  farthest  limit  of  the  Sun's  force,  there  to  be  lost 
to  us  and  never  to  return,  which  it  seems  would  be  the  more 
likely  result  if  thrown  in  the  direction  contrary  to  which 
the  Sun  is  traveling  in  the  heavens. 

A  comet  might  be  drawn  farther  into  the  stream  of  the 
Sun's  force  than  otherwise  by  the  attraction  of  some  of  the 
planets  when  passing  in  the  region  of  them,  and  if  receding 
from  the  Sun  would  consequently  be  thrown  farther  away, 
making  a  more  elliptical  orbit,  and  also  extending  the  time 
for  the  comet's  return.  These  seem  to  be  the  circumstances 
attending  the  comet  which  appeared  in  1779,  the  orbit  of 
which  indicated  short  and  quite  regular  periods,  when  it  was 
drawn  by  the  attraction  of  Jupiter  well  into  the  Sun's  force, 
and  its  orbit  so  changed  that  it  has  not  since  been  seen. 

When  a  comet  is  approaching  the  Sun  its  velocity  is  con- 
stantly increasing,  until  it  is  thrown  off  again  by  the  Sun's 
force,  when  its  velocity  decreases,  until  the  force  is  spent 
which  sent  it  away,  after  which  it  usually  returns  to  the 
Sun,  and  in  the  same  manner  as  before.  As  the  ball  which 
is  thrown  in  the  air  will  return  with  the  same  velocity  as 
that  with  which  it  ascended,  so  the  planets  and  comets  re- 
turn to  their  perihelion  with  about  the  same  velocity  as 
that  at  which  they  were  forced  away. 

The  history  of  comets,  as  a  whole,  according  to  general 
observations,  defines  pretty  clearly  the  direction  of  the  force 
of  the  Sun,  but  gives  us  no  idea  of  the  eddies  of,  or  the  di- 
viding and  disseminating  of,  the  Sun's  force  or  current,  at 
its  extreme  edge,  other  than  the  planetary  and  cometary 
action  which  gives  evidence  that  the  force  is  continually 
falling  out  of  the  stream  at  its  sides,  all  the  way  along,  from 
the  center,  or  near  the  Sun,  to  its  extreme  edge,  and  then 
returns  toward  the  Sun  only  to  be  thrown  off  again  in  a 
manner  similar  to  the  air,  by  a  rotary  blower. 


52  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 


Among  the  many  questions  of  more  or  less  importance 
that  arise  while  considering  the  motions  of  the  Sun  and 
planets  by  the  foregoing  theory  and  illustrations,  that  of  the 
tides  becomes  one  of  much  interest,  for  it  is  well  known  by 
those  who  have  had  opportunities  to  observe  and  investi- 
gate that  the  equatorial  diameters  of  most,  if  not  all,  of  the 
planets  which  revolve  on  their  axes  are  considerably 
greater  than  their  polar  diameters,  which  is  accounted  for 
by  no  other  theory  than  the  resulfor  effect  of  the  centrifugal 
force  that  is  developed  by  the  velocity  with  which  the 
planets  rotate  on  their  axes  and  the  act  of  throwing  off  by 
this  force  the  substance  or  material  of  which  they  are  com- 
posed while  in  a  fluid  or  movable  condition  farther  from 
the  center  of  the  planets  in  the  region  of  their  equators  than 
elsewhere  on  their  surfaces.  The  tidal  theory,  which  most 
authors  have  accepted  and  which  is  now  generally  taught 
in  the  later  astronomical  text-books,  appears  defective  if 
the  cause  is  examined  in  relation  to  the  Moon,  when  in  dif- 
ferent parts  of  its  orbit  around  the  Earth.  As  commonly 
taught,  the  Moon  draws  the  fluid  portions,  or  the  water,  on 
the  Earth  on  the  side  of  the  Earth  toward  the  Moon,  a 
little  higher  than  the  average  height,  thus  making  the 
higher  tide,  and  at  the  same  time  drawing  the  Earth,  not 
quite  so  much,  but  partially,  away  from  the  water  on  the 
opposite  side  from  the  Moon,  thus  causing  the  water  to  be 
drawn  up  to  a  ridge  which  forms  the  smaller  wave  on  the 
opposite  side  of  the  Earth  from  the  larger  one.  The  objec- 
tions to  this  theory  are  so  numerous,  and  the  theory  is  so 
much  at  variance  with  natural  law,  that  only  a  few  of  the 
positions  of  the  Moon  in  relation  to  the  Earth  will  be  re- 
ferred to.  It  should  be  borne  in  mind  that  the  Moon  is 
traveling  comparatively  slowly  and  quite  regularly  around 
the  Earth,  going  only  about  one  twenty -ninth  of  its  orbital 
distance,  or  between  twelve  and  thirteen  degrees  of  its  en- 
tire circuit,  in  twent}^-four  hours,  and  which  is  only  about 
thirty-five  miles  per  minute,  not  taking  into  account  the 
distance  that  it  travels  along  the  Earth's  orbit  in  the  same 


TIDES.  53 

time.  The  attractive  influence  of  the  Moon  on  the  Earth 
is  in  accordance  with  and  in  proportion  to  its  distance  from 
it.  When  in  perigee  the  attraction  is  greatest,  and  least  in 
apogee.  The  Moon  arrives  at  these  positions  gradually  at 
intervals  of  a  little  more  than  fourteen  and  one-half  days. 

If  the  theory  in  regard  to  the  cause  of  the  tides  or  the 
way  they  are  produced,  as  popularly  taught,  is  correct,  then 
authors  have  apparently  overlooked  the  fact  that  the  Earth 
must  be  drawn  a  little  for  several  days  from  its  natural 
orbital  position  by  the  Moon  at  the  time  of  the  lunar  tides, 
before  and  after  the  time  of  the  new  and  full  moon,  and 
also  must  be  drawn  correspondingly  by  the  Sun  and  always 
in  the  same  direction,  when  the  tides  are  produced  by  it; 
and  in  neither  case  do  they  tell  us  how  or  when  the  Earth 
gets  back  into  its  natural  orbital  position  again  after  any 
given  meridian,  by  the  Earth's  rotation  on  its  axis,  has 
passed  the  attractive  influence  of  the  Moon  or  Sun.  If  there 
has  ever  been  any  recoil  detected  in  the  forces  which  pro- 
duce the  tides,  the  observers  have  failed  to  give  a  record  of 
it  to  the  public. 

As  the  Moon  apparently  moves  to  and  from  any  position 
at  the  rate  of  about  thirty-five  miles  per  minute  it  evi- 
dently would  cause  no  sudden  movement  of  the  Earth 
towards  it,  much  less  one  that  would  be  sufficient  to  leave 
its  waters  behind  it.  To  examine  this  prevalent  theory  in 
regard  to  the  tides,  as  popularly  taught,  the  objections  are 
more  easily  explained  by  reference  to  the  conditions  which 
are  claimed  to  exist  and  to  occur  at  all  the  points  of  the 
Moon's  orbit  while  the  Moon  is  passing  around  the  Earth, 
but  reference  will  be  made  to  only  a  few  of  the  positions  of 
the  Moon  in  which  it  produces  the  more  prominent  results 
and  in  which  the  angles  or  lines  of  attraction  of  the  Sun 
and  Moon  to  the  Earth  are  the  least  and  greatest,  leaving 
the  intermediate  graduating  effect  or  result  for  the  reader 
to  proportion  according  to  the  position  that  the  Moon  may 
be  presumed  to  occupy  at  the  time.  During  the  time  of  a 
few  successive  tides,  when  the  Moon  is  between  or  nearly 
between  the  Earth  and  the  Sun,  the  water  on  the  Earth's 
surface  must  be  drawn  toward  it  quickly  to  produce  the 


54  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

greater  tides,  and  at)  the  same  time  the  Earth  must  be  sud- 
denly drawn,  but  not  quite  so  far,  toward  the  Moon,  in 
order  to  leave  the  water  behind  it  to  form  the  tide  which 
occurs  at  the  same  time  on  the  opposite  side  of  the  Earth 
from  the  Moon,  and  this  same  sudden  jerking  process  of  the 
Earth  out  of  its  regular  orbit,  when  it  is  traveling  at  the 
rate  of  about  eleven  hundred  and  ten  miles  per  minute,  by 
the  Moon  which  is  only  about  one-fiftieth  of  its  bulk,  must 
occur  oftener  than  once  at  each  revolution  of  the  Earth  in 
relation  to  the  Moon,  to  produce  the  several  tides  which 
occur  on  different  parts  of  the  Earth's  surface  while  the 
Earth  rotates  on  its  axis  once.  If  the  Earth  is  drawn  from 
its  orbit  when  the  tide  occurs  in  the  Atlantic  ocean,  it  must 
be  drawn  likewise  when  the  tide  occurs  in  the  Pacific  ocean, 
and  again  when  it  occurs  in  the  Indian  ocean.  So  we  see  that 
at  three  successive  times  at  every  rotation  of  the  Earth  upon 
its  axis  our  planet  must  be  drawn  suddenly  from  its  orbital 
position  by  a  force  infantile  as  compared  with  the  Earth, 
and  no  system  is  claimed  or  advanced  by  which  it  may  re- 
turn to  its  natural  orbital  position  again.  When  the  Moon 
is  at  or  near  the  position  of  first-quarter,  it  is  on  or  near 
the  Earth's  orbit,  and  directly  behind  or  in  the  rear  of  the 
Earth,  while  the  Earth  is  traveling  at  its  usual  speed  right 
away  from  the  Moon,  yet  we  are  asked  to  believe  that  the 
water  on  the  Earth's  surface  on  three  separate  ocean  spaces 
is  drawn  back  three  times  at  each  one  of  the  Earth's  rota- 
tions, or  once  for  each  ocean  to  each  rotation,  in  order  to 
produce  the  tides  in  the  different  oceans ;  and  also  to  believe 
that  the  Earth  is  checked  suddenly  enough  in  its  orbital 
velocity  three  times  during  one  rotation  on  its  axis,  in  order 
that  the  water  on  the  opposite  side  of  the  Earth  from  the 
Moon  may  apparently  pass  on  a  little  ahead  of  the  Earth 
in  the  direction  in  which  the  Earth  is  traveling,  to  form  the 
tide  on  the  opposite  side  of  the  Earth  from  the  larger  one. 
The  effect  produced  on  the  Earth  by  the  Moon  when  it  is  on 
the  opposite  side  of  the  Earth  from  the  Sun,  or  about  the 
times  of  being  full,  is  similar  to  the  effect  to  that  which  is 
produced  when  the  Moon  is  new,  or  between  the  Earth  and 
the  Sun,  it  being  diminished  by  the  amount  of  the 


TIDES.  55 

Sun's  attractive  influence  on  the  Earth  in  causing  the 
solar  tide.  When  the  Moon  is  at  or  near  the  last  of  the 
third  or  the  beginning  of  the  fourth  quarter,  it  is  just  in 
advance  of,  or  in  front  of,  the  Earth,  with  the  Earth  rushing 
on  toward,  or  nearly  toward,  it  for  several  days  at  its  usual 
speed,  and  at  that  time,  the  Moon  must  draw  the  water 
which  is  on  the  side  of  the  Earth  toward  and  nearest  it  a 
little  faster  than  the  Earth  is  traveling  in  its  orbit  to  pro- 
duce the  larger  tide,  and  at  the  same  time  it  must  cause  the 
Earth  to  suddenly  hasten  its  speed  sufficiently  to  leave  a 
ridge  of  water  on  the  opposite  side,  which  is  shown  as  the 
smaller  lunar  tide,  which  occurs  twelve  hours  and  about 
twenty-six  minutes  after  the  larger  one,  and  these  effects 
must  be  produced  three  times  to  each  rotation  of  the  Earth 
on  its  axis,  in  order  that  one  tide  may  be  produced  in  each 
of  the  oceans  mentioned,  and  in  which  the  tides  regularly 
occur.  The  same  inconsistencies  appear,  no  matter  in  what 
position  the  Moon  may  be  to  the  Earth,  when  the  cause  of 
the  tides,  as  taught  in  text-books,  is  sought  for  in  relation 
to  it.  So  the  author  feels  justified  in  leaving  this  theory  as 
he  found  it,  and  looking  for  a  cause  for  the  tides  that  ap- 
pears to  be  more  in  harmony  with  the  operation  of  the  nat- 
ural forces  around  us. 

The  fact  that  every  meridian,  or  part  of  the  Earth's  sur- 
face, is  being  constantly  and  rapidly  presented  toward  the 
Sun  and  Moon,  should  not  be  overlooked,  for  it  is  in  con- 
nection and  unison  with  these  conditions  that  the  tides 
occur.  The  attractive  influence  of  the  Moon  as  causing  the 
tides,  is  acting  upon  the  Earth  in  the  same  manner  at  all 
times,  and  varying  in  degree  as  the  Moon  gradually  ap- 
proaches and  leaves  its  perigee  or  apogee,  and  changes  its 
position  in  relation  to  the  Earth's  surface  as  the  Earth  ro- 
tates on  its  axis.  The  effect  of  the  attractive  influence  on 
the  Earth  which  causes  the  tides  is  always  found  in  the 
same  relative  position  to  the  Sun  or  Moon ;  consequently 
there  can  be  no  sudden  movement  to  produce  conditions 
which  already  exist. 

Figure  V  shows  the  relative  position  of  the  tides  to  the 
Sun  and  Moon,  as  being  produced  by  their  jattraction  and 


56  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

the  centrifugal  force  of  the  Earth,  as  developed  by  the  ro- 
tation on  its  axis.  The  pole  of  the  Earth  is  shown  as  being 
in  a  horizontal  position,  with  the  tides  shown  a  few  degrees 
from  and  after  passing  the  line  of  attraction  of  the  Sun  and 
Moon.  The  solar  tide  alwa}Ts  remains  in  the  same  relative 
position  to  the  Sun.  The  lunar  tide  always  remains  in  the 
same  relative  position  in  advance  of  the  Moon,  but  the 
rotation  of  the  Earth  on  its  axis  carries  any  given  meridian 
on  from  the  Moon  to  the  position  of  the  lunar  tide  in  the 
time  that  the  tide  appears  after  the  Moon  has  passed  a  me- 
ridian ;  this  causes  the  appearance  of  the  tide  following  the 
Moon.  As  the  Moon  passes  around  the  Earth  the  lunar  tide 
advances,  and  passes  through,  or  over,  the  solar  tide,  about 
the  time  of  new  moon,  or  when  the  Moon  passes  between  the 
Earth  and  the  Sun,  and  also  when  the  Earth  is  between 
the  Moon  and  the  Sun ;  at  these  times  the  solar  and  lunar 
tides  mingle  together  and  form  one  which  about  equals  the 
solar  and  lunar  tides  in  volume. 

The  rise  and  fall  of  the  tide  waves  seem  to  add  still  more 
proof  of  the  correctness  of  the  theory  of  centrifugal  force, 
as  applied  to  our  Earth  and  as  illustrated  by  Figure  VI. 

The  tides  appear  to  follow  the  Moon  and  Sun  at  certain 
and  regular  periods  of  time,  after  the  Sun  or  Moon  have  ap- 
parently passed  a  meridian,  and  also  that  they  occur  again 
at  regular  intervals  when  the  Moon  or  Sun  is  on  the  oppo- 
site side  of  the  Earth.  The  small  tide  that  follows  the  Sun 
varies  in  height  and  volume,  according  to  the  distance  of 
the  Sun,  the  same  as  the  lunar  tide.  If  the  rapid  rotation 
of  the  planets  on  their  axes,  at  any  time  of  their  existence, 
would  have  caused  a  greater  equatorial  than  polar  diam- 
eter, the  same  law  would  control,  in  the  same  manner,  the 
fluid  parts  of  the  planets  at  the  present  time;  and  this 
seems  to  be  the  case  in  regard  to  our  own  planet,  whose 
surface  is  about  three-quarters  fluid,  and  in  constant  mo- 
tion, while  the  surface  at  the  equator  is  about  thirteen  miles 
farther  from  the  center  than  is  the  surface  of  the  Earth  at 
the  poles. 

The  wheel,  as  shown  in  Figure  VI,  is  the  same  in  princi- 
ple as  the  one  constructed  and  tried  by  the  author,  which 


A  WHEEL  REPRESENTING  THE  EARTH 


TIDES.  59 

is  intended  to  illustrate  the  theory  of  centrifugal  force,  as 
applied  to  our  Earth  in'  causing  the  tides. 

•  The  wheel,  as  constructed,  was  about  twelve  feet  in  diam- 
eter, with  levers  attached  to  the  rim,  with  a  hinge  and 
weights  attached  to  the  end  of  the  levers.  The  weights 
were  held  close  to  the  rim  of  the  wheel  by  the  aid  of  elas- 
tics. The  weights  were  equal  in  number  and  weight,  so 
that  the  wheel  was  equally  balanced,  and  as  attached  to  the 
rim  of  the  wheel  were  intended  to  represent  the  water,  or 
any  substance  that  could  be  moved  from  its  natural  place,  or 
position  of  rest,  by  the  centrifugal  force  of  the  Earth,  in  con- 
nection with  the  attraction  of  any  external  body,  as  the 
Moon  or  Sun.  The  tension  on  the  elastics  was  equal, 
and  sufficient  to  hold  the  weights  firmly  to  the  rim  of  the 
wheel,  when  not  in  motion.  The  wheel,  as  a  whole,  was  in- 
tended to  represent  the  Earth,  with  the  water  of  the  Eai'th 
as  being  agitated  by  the  attraction  of  the  Moon  or  Sun,  as 
seen  in  the  tidal  action.  The  elastics,  as  shown,  holding 
-the  weights  to  the  rim  of  the  wheel,  represent  the  law  of  at- 
traction, or  gravitation,  of  the  Earth,  or  -centripetal  force, 
as  holding  the  water  to  the  Earth's  surface.  The  Earth's 
attraction  on  the  wheel  represents  the  attraction  of  the 
Moon  or  Sun  on  the  Earth,  only  in  a  far  greater  degree. 
When  the  wheel  was  placed  in  a  vertical  position  (or  such 
position  as  the  satellites  bear  to  their  primaries,  and  all  of 
the  planets  to  the  Sun),  and  revolved  at  a  moderate  speed, 
the  centrifugal  force  of  the  wheel  would  overcome  the  cen- 
tripetal force  of  the  elastics,  and  the  weights  would  first 
commence  to  leave  the  rim  of  the  wheel  soon  after  they 
passed  the  horizontal  diameter  on  the  descending  side  of 
the  wheel,  from  which  point  the  weights  would  gradually 
increase  in  distance  from  the  rim,  until  they  reached  a 
point  about  half  way  between  the  vertical  diameter  on  the 
lower  side  and  the  horizontal  diameter  on  the  ascending 
side  of  the  wheel.  After  this  latter  point  was  reached,  the 
attraction  of  the  elastics  would  cause  the  weights  to  return 
quickly  to  the  rim  of  the  wheel,  and  to  remain  there  in 
their  natural  positions  until  they  again  passed  the  horizon- 
tal diameter  on  the  descending  side,  when  they  would  leave 


60  MECHANICS   APPLIED   TO   THE   SOLAR   SYSTEM. 

the  rim  of  the  wheel  as  before.  This  greatest  throwing-off 
point  corresponds  well  with  the  position  of  high  tide  on  the 
Earth  and  the  Moon  at  any  given  meridian. 

In  the  relative  position  on  the  wheel  where  the  low  tide 
should  occur  on  the  Earth,  twelve  hours  and  about  twenty- 
six  minutes  after  the  high  tide,  or  on  the  opposite  side  of 
the  Earth  from  the  high  tide,  there  was  no  perceptible  in- 
clination of  the  weights  to  leave  the  rim  of  the  wheel, 
thereby  showing  that  theories  which  teach  us  that  the 
smaller  tide  is  necessary  to  counter-balance  the  larger  one, 
that  first  follows  the  Moon  or  Sun,  may  be  erroneous. 

The  test  made  with  the  wheel,  as  shown  in  the  accompa- 
nying figure  and  as  described,  would  seem  to  prove  that 
the  tidal  waves  are  developed  by  the  centrifugal  force  of 
the  Earth,  whose  tendency  it  is  to  throw  off  toward  any 
object  which  has  an  attraction  for  it,  and  so  we  have  the 
largest  wave  occurring  at  the  point  indicated,  for  it  is  there 
that  the  greatest  accumulated  effect  of  the  Moon's  attractive 
influence  is  observed.  After  passing  this  point  on  the 
Earth's  surface,  or  when  coming  in  contact  with  the  shores 
of  continents  which  are  rigid  and  unyielding,  the  water  is 
no  longer  under  the  influence  of  the  Moon,  and  then  it  seeks 
its  natural  equilibrium,  or  level,  on  the.  Earth,  and  in  doing 
so  we  see  the  second,  or  smaller  tide,  is  produced,  which 
may  travel  a  long  distance  with  but  little  decrease  of  vol- 
ume, because  of  the  noncompressibility  of  water.  This  the- 
ory may  also  explain  why  the  tides  on  all  eastern  shores 
are  higher  than  on  the  western  shores,  and  whether  or  not 
the  wave  that  approaches  the  western  shores  is  only  a  re- 
action of  the  one  which  previously  passed  to  the  eastern 
shore  in  the  same  sea,  which,  if  proved  to  be  the  case,  would 
account  for  the  tides  running  from  west  to  east  into  the 
bays,  harbors,  etc.,  of  the  western  shores  of  the  continents. 
If  the  tide  waves  on  the  western  shores  are  only  the  reaction 
of  a  greater  one  going  the  other  way,  then  (according  to  this 
theory),  it  would  be  safe  to  assume  that  the  high  tide  on  all 
western  shores  should  about  equal  the  one  second  in  height 
on  the  eastern  shores.  By  consulting  a  map  of  the  world 
or,  better  still,  a  globe  or  sphere  with  the  map  of  the  world 


TIDES.  61 

upon  it,  and  observing  the  open  space  over  which  the  tide 
wave  passes,  from  east  to  west,  we  can  get  a  better  idea  of 
the  force  and  direction  of  the  wave,  and  its  terminations 
against  the  continents  and  the  final  distribution  of  the 
water,  as  shown  by  the  ocean  currents,  than  by  almost  any 
other  means  that  we  have.  It  can  there  be  seen  that  the  wave 
can  commence  to  form  along  the  eastern  edge  of  the  Atlantic 
soon  after  the  Moon  has  passed  the  meridian,  and  appear  to 
follow  it,  with  but  little  interruption,  until  it  comes  in  con- 
tact with  the  shores  of  the  American  continent,  where  it 
will  first  reach  the  most  eastern  point  of  land,  which  is  at 
Cape  St.  Roque,  the  eastern  projection  of  Brazil,  and  near 
the  equator.  It  is  here  near  the  equator  that  the  tendency 
of  the  Earth  is  to  throw  off  by  its  rotation,  more  than  north 
or  south  of  it,  because  of  its  greater  circumference  in  this 
part.  So  it  follows  that  the  supply  that  is  drawn  here  must 
come  from  parts  of  the  sea  which  are  situated  each  side  of 
the  equator,  or  from  toward  the  poles  of  the  Earth,  and  must 
be  drawn  toward  the  equator,  as  shown  by  the  ocean  currents. 
As  the  wave  in  its  progress  westward  is  interrupted  by  the 
shoals,  islands,  continents,  etc.,  the  sea  becomes  higher  in 
places  than  it  otherwise  would  be,  and  then  is  forced  to 
seek  an  equilibrium  in  the  directions  where  there  is  the 
least  resistance.  One  of  the  most  prominent  is  seen  in  the 
warm  current  of  the  Gulf  Stream  that  flows  northward  from 
near  the  mouth  of  the  Gulf  of  Mexico,  after  it  has  been 
driven  into  the  vee  (V)  shaped  form  in  the  Atlantic  Ocean, 
which  is  formed  by  the  northeast  shore  of  South  America, 
extending  from  Cape  St.  Roque  to  the  north  of  Yucatan, 
and  the  southeast  shore  of  North  America,  from  New  Found- 
land  to  the  Florida  Reefs.  Another,  less  prominent,  is  seen 
in  the  vee  (V)  form  of  the  Pacific  Ocean,  which  terminates 
in  the  China  Sea. 

Another  simple  and  easy  test  can  be  made  by  pouring  a 
small  quantity  of  water  on  a  grindstone  or  similar  wheel 
and  revolving  it  fast  enough  so  that  the  water  will  not  have 
time  to  collect  and  drop  from  the  lower  surface,  nor  yet  fast 
enough  to  throw  the  water  off,  and  conditions  wrill  be 
obtained  under  which  can  be  seen  a  quantity  of  water  con- 


62  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

tinually  collecting  near  the  point  on  the  edge  of  the  revolv- 
ing body  corresponding  with  the  location  on  the  wheel 
where  the  weights  were  thrown  the  farthest  away,  and  also 
corresponding  to  the  position  of  the  tide  after  any  given 
meridian  of  the  Earth  has  passed  its  nearest  point  of  attrac- 
tion to  the  Moon  or  Sun.  The  author  has ' not  taken  into 
consideration  the  varying  times  that  it  takes  the  tides  to 
run  into  the  various  inlets,  channels,  etc.,  but  has  formed 
his  conclusion  from  effects  which  have  been  observed  as 
nearly  as  possible  in  the  open  sea. 

This  theory,  if  followed,  would  also  imply  that  if  the  speed 
of  the  Earth  on  its  axis  could  be  increased  sufficiently,  the 
water  would  be  thrown  from  its  surface  at  nearly  the  point 
of  high  tide,  in  a  somewhat  curved  line  toward  the  Moon, 
were  it  not  for  the  fact  that  the  same  law  that  would  throw 
the  water  off  from  the  Earth  already  keeps  the  Moon  at 
its  present  distance  from  the  Earth  and  in  its  orbit,  and 
an  increased  velocity  of  the  Earth  on  its  axis  would 
throw  the  Moon  proportionately  farther  away.  The  at- 
traction of  the  Moon  would  then  be  lessened  in  propor- 
tion, and  the  tidal  effect  would  probably  be  about  the  same 
as  we  see  around  us  at  the  present  time.  This  same  law 
also  implies  that  an  increase  or  decrease  in  the  speed  of  the 
Sun  on  its  axis  would  enlarge  or  decrease  correspondingly 
all  of  the  orbits  of  the  planets  of  our  solar  system. 

EARTHQUAKES. 

It  is  a  natural  law  in  regard  to  all  rotating  bodies  that 
the  farther  from  the  axis  or  center  of  a  revolving  rotating 
body  or  sphere,  and  the  heavier  the  materials,  the  greater 
will  be  the  effect  of  the  centrifugal  force  in  throwing  off 
particles  or  substances  from  a  rotating  body.  This  would 
suggest  that  the  higher  the  continents  or  land  portions,  the 
greater  would  be  the  centrifugal  effect,  so  it  seems  in  accord 
with  this  law  that  the  Moon  should  exert  a  like,  if  not 
greater,  influence  on  the  higher  parts  of  the  Earth  than  it 
does  on  the  water,  where  the  effect  is  so  readily  and  regu- 
larly seen.  Although  the  materials  of  the  continents  are 
rigid  and  immovable,  yet  it  seems  that  there  must  be  an 


EARTHQUAKES.  63 

immense  strain  upon  them  every  time  they  are  presented 
by  the  Earth's  rotation  to  any  external  body  of  attraction. 
A  continuous  vibration  is  known  to  rend  the  most  subtan- 
tial  structures,  if  not  carefully  watched,  repaired  and  pro- 
tected, therefore  it  would  be  difficult  to  prove  that  this  same 
law  of  centrifugal  force  in  connection  with  the  attraction  of 
the  Sun  and  Moon  does  not  aid,  to  some,  if  not  to  a  great, 
extent,  in  producing  our  earthquakes.  There  seems  to  be  no 
way  of  ascertaining  the  time  that  an  earthquake  is  going  to 
occur,  for  if  they  are  caused  by  the  centrifugal  force  of  the 
Earth,  there  is  no  way  known  at  present  to  compute  that 
force,  or  to  ascertain  the  amount  of  power  that  is  developed 
at  the  Earth's  surface,  or  the  amount  that  is  or  would  be 
required  to  cause  the  earthquakes  in  the  different  localities 
where  they  have  often  occured.  The  fact  of  their  being 
more  frequent  in  some  sections  than  others  may  depend 
somewhat  upon  the  nature  of  the  formation  of  that  locality. 
The  stronger  parts  of  the  Earth's  surface  may  withstand  the 
vibrations  for  hundreds  and  even  thousands  of  years  before 
the  strain  will  be  made  known  by  the  earthquake,  and  after 
the  earthquake  has  occurred  there  may  be  a  long  or  short 
period  of  time  before  the  next  one  occurs,  which  would 
probably  depend  on  the  solidity  and  fixed  positions  of 
the  earthy  matter.  This  strain  has  not  been,  nor  can  it  be, 
easily  calculated;  for,  as  in  the  bridge  which  sustains  a 
certain  weight  with  safety  when  new,  and  which  gives  way 
under  the  same  pressure  after  seasons  of  vibrations  and 
molecular  change,  so,  after  repeated  exposures  of  the 
continents  or  land  portions  of  the  Earth  to  the  attractive 
influence  of  the  Moon  or  Sun,  it  seems  but  natural  that  occa- 
sionally there  should  occur,  in  some  manner,  a  perceptible 
result  of  that  power  which  is  applied  so  often  and  with  such 
regularity  to  our  planet.  In  volume  XXXI  of  the  Popular 
Science  Monthly  (page  397),  it  is  stated  that  M.  Perry  in  his 
researches,  has  shown  that  more  earthquakes  occur  when 
the  Moon  is  in  conjunction  and  opposition  than  at  interme- 
diate times,  and  still  more  when  it  is  directly  between  the 
Earth  and  the  Sun,  and  when  the  Moon  is  nearest  the 
Earth  than  when  not  in  those  relative  positions  to  our  planet. 


64  MECHANICS   APPLIED    TO   THE   SOLAR    SYSTEM, 

On  page  398,  same  volume  and  same  article,  Prof.  G.  H. 
Darwin,  F.  R.  S.,  says  that  earthquakes  are  more  frequent  in 
the  winter  than  in  the  summer  of  the  northern  latitudes.  It 
is  also  a  well-known  fact  that  earthquakes  occur  oftener  with- 
in forty-five  degrees  of  the  equator  than  farther  north  or 
south  of  it. 

The  statements  of  the  above  eminent  and  popular  authors 
seem  to  fully  support  the  theory  of  throwing  off  by  centri- 
fugal force,  as  herein  set  forth,  and  as  the  author  has  in- 
tended to  show  by  the  attractive  force  of  the  Sun  or  Moon, 
or  of  the  Sun  and  Moon  combined,  in  producing  the  tides, 
which  vary  in  height  according  to  the  distance  of  the  Sun 
or  Moon.  In  them  we  see  the  effect  of  the  attractive  force 
of  the  Sun  and  Moon  to  be  increased  or  diminished  in  pro- 
portion to  the  greater  or  lesser  distance  that  they  are  from 
the  Earth.  As  the  Sun  is  somewhat  nearer  the  Earth  in  our 
winter  than  in  our  summer,  so  we  may  expect  results  that 
will  correspond  with  the  attraction  caused  by  the  increased 
or  decreased  distance  from  the  Sun,  and  which  would  har- 
monize with  the  observations  of  Prof.  G.  H.  Darwin  in  his 
researches. 

HEAT. 

The  question  also  arises  whether  much  of  the  heat  of  the 
Earth  may  not  be  due,  to  some  extent,  to  the  centrifugal 
force  of  the  Sun  acting  upon  the  Earth's  surface.  Although 
most  authors  claim  that  the  heat  on  the  surface  of  the 
Earth,  whether  little  or  great,  is  in  proportion  to  the  num- 
ber of  the  Sun's  rays  that  fall  upon  each  square  inch  of 
surface,  yet  we  know  that  the  Earth  is  several  million  miles 
nearer  the  Sun  in  our  winter  than  in  our  summer,  and  in 
many  locations  the  land  is  so  formed  or  shaped  that  as 
many,  and  sometimes  more,  rays  fall  to  the  square  inch  in 
winter  than  in  the  summer,  yet  there  is  much  less  heat. 
If  the  theory  that  the  Earth  is  slowly  cooling  down  is  cor- 
rect, then  it  follows  that  there  must  be  a  system  or  an 
opportunity  by  which  the  internal  heat  of  the  Earth  may 
escape  or  radiate  away  into  the  space  which  surrounds  it. 
The  foregoing  theory  and  illustrations  are  intended  to  show 
the  manner  in  which  the  repelling  force  of  the  Sun  is  acting 


HEAT.  65 

upon  the  planets,  and  the  results  that  are  natural  to  follow 
such  action.  The  repelling  action  of  the  Sun  implies  a 
pressure  exerted  by  the  Sun  upon  the  bodies  upon  which 
it  is  operating.  The  greatest  heat  is  where  the  force  rays 
of  the  Sun  come  in  contact  with  the  main  part  of  the 
Earth's  surface  the  more  squarely,  and  it  seems  but  a  nat- 
ural effect  that  in  parts  of  the  Earth  near  the  equator  the 
heat  of  the  Earth  would  have  but  little  chance  to  escape, 
while  near  the  poles,  or  any  part  of  the  Earth  which  may 
be  so  turned  from  the  Sun  that  its  rays  will  strike  it 
obliquely,  the  heat  of  the  Earth  would  meet  with  little 
obstruction  in  escaping,  while  perhaps  the  force  rays  of 
the  Sun  in  passing  by  or  near  the  poles  might  aid  in  carry- 
ing off  some  of  the  Earth's  heat  into  space.  The  snow- 
capped mountains  of  the  tropics,  which  are  above  the 
suppressed  heat  of  the  Earth,  are  so  situated  and  formed 
that  the  heat  that  is  within  them  can  easily  radiate  or  be 
driven  away  instead  of  being  driven  back  or  held  to  the 
surface  of  them,  as  it  is  in  the  lower  or  flat  parts  of  the  Earth, 
where  the  force  rays  of  the  Sun  are  beating  more  squarely 
on  the  surface  of  the  Earth  and  holding  the  heat  down,  or 
continually  forcing  it  back  to  the  Earth's  surface. 

Prof.  Tyndall  demonstrates  in  his  lectures  on  heat  that 
there  are  rays  of  light  and  heat  separate  and  distinct  from 
each  other,  and  that,  with  proper  means  or  arrangements, 
the  light  rays  can  be  intercepted  and  the  heat  rays,  as  he 
terms  them,  will  pass  on  the  same  as  if  the  light  rays  were 
not  shut  off,  or  the  heat  may  be  absorbed,  and  the  light  rays 
will  pass  on  as  if  there  had  been  no  interference  with  the 
heat  rays.  The  velocity  of  the  sunlight  is  popularly  known 
to  be  about  186,000  miles  per  second,  but  the  author  has 
seen  no  estimate  or  calculation  of  the  velocity  of  the  heat 
rays.  Experiments  have  shown  that  heat  may  be  devel- 
oped by  submitting  substances  to  pressure  or  friction. 
While  the  attraction  of  the  Sun  is  drawing  the  planetary 
bodies  toward  it,  they  are  held  in  position  by  a  repelling 
force  which  keeps  them  a  certain  distance  away  from  it, 
and  it  is  not  yet  proved  that  there  is  no  heat  developed  by 
this  repelling  force  acting  on  or  against  planetary  surfaces. 


60  MECHANICS    APPLIED    TO    THE    SOLAR    SYSTEM. 

Nor  is  it  proved  that  there  is  no  heat  produced  by  the  fric- 
tion of  the  Sun's  force  on  entering  and  passing  through  our 
atmosphere.  There  seems  little  reason  to  expect  to  find 
heat  in  the  open  space  of  the  heavens  where  the  Sun's  force 
rays  are  not  interfered  with,  unless  at  or  near  the  Sun's 
equatorial  plane.  The  sunlight  which  is  reflected  from  the 
Moon  seems  to  contain  no  heat,  thus  showing  that  the  heat 
produced  by  the  Sun  at  or  on  the  Moon's  surface  must 
be  radiated  from  or  absorbed  by  it.  The  attraction  of 
the  Earth  for  the  Moon  is  counterbalanced  by  the  repelling 
force  of  the  Earth,  which  is  always  acting  on  the  same  side 
of  the  Moon,  and  if  there  is  any  heat  developed  on  the 
Moon's  surface  by  this  repelling  force,  the  temperature  on 
the  side  of  the  Moon  which  is  turned  toward  the  Earth  may 
be  considerably  higher  than  has  generally  been  supposed. 
As  the  Moon  travels  around  the  Sun  in  a  slightly  scolloped 
path  or  orbit,  and  rotates  on  its  axis  only  once  in  about 
twenty-nine  and  a  half  days,  it  is  evident  that  the  throwing 
off  force  from  it  must  be  very  small,  and  whatever  there  is 
must  be  thrown  from  its  farther  side,  in  part  by  its  apparent 
swinging  motion  around  the  Earth,  similar  to  the  water 
which  may  be  thrown  from  a  sponge  when  attached  to  the 
end  of  a  string  and  swung  in  a  circle. 

Authors  have,  from  time  to  time,  attempted  to  demon- 
strate the  cause  of  the  Sun's  heat,  some  offering  as  a  reason 
that  the  Sun  must  be  gradually  shrinking  by  its  own  attrac- 
tion, resulting  in  the  heat  which  is  claimed;  for  it.  Some 
have  given  estimates  of  the  amount  of  contraction  which 
would  be  necessary  each  year  to  correspond  to  th'3  amount  of 
the  heat  which  they  have  calculated  must  radiate  from  the 
Sun's  entire  surface  in  the  same  time.  Some  presume  the  Sun 
to  be  surrounded  by  aerolites  and  meteoric  substances,  etc., 
which  are  constantly  falling  to  the  Sun  from  every  direction 
in  countless  millions,  thus  producing  the  Sun's  heat  by  their 
velocities  and  impact,  combustion,  etc.,  on  the  Sun's  surface, 
all  combining  to  produce  the  heat  of  the  Sun,  which  is  said 
to  be  radiating  equally  from  every  part  of  its  surface  and 
in  the  same  direction  as  the  sunlight.  Some  authors  have 
undertaken  to  estimate  the  entire  amount  of  the  Sun's  heat 


HEAT.  67 

by  assuming  that  the  same  amount  is  being  radiated  alike 
from  every  part  of  its  surface,  and  they  base  their  estimates 
on  what  is  received  in  certain  locations  on  the  Earth's  sur- 
face. These  estimates  are,  probably,  a  great  deal  too  much ,  if 
the  theory  that  the  Sun  is  throwing  off  influences  by  centrifu- 
gal force  is  correct.  For  heat,  unlike  light  rays,  can  be  changed 
from  a  direct  course,  or  line,  by  and  in  the  direction  of  a 
passing  current,  as  shown  by  the  heat  of  the  simoons  of 
the  desert,  or  the  moderated  temperature  in  countries  of  the 
northern  hemisphere,  caused  by  the  flow  of  ocean  currents 
from  the  tropic  regions,  or  as  may  be  shown  by  the  heat 
which  may  be  driven  off  with  the  air  in  any  direction  from 
a  heated  body. 

The  author  admits  that  the  heat  may  be  radiating 
from  the  Sun's  entire  surface,  in  nearly  the  same  amount, 
but  claims  that  after  it  radiates  a  certain  distance  from  its 
surface  it  is  met  by  the  inflow  of  the  influences  which  are 
being  constantly  drawn  toward  the  Sun  and,  from  there,  most 
of  the  heat  is  diverged  or  drawn  toward  the  Sun's  equatorial 
region,  to  be  carried  off  in  the  current  of  the  Sun's  force,  as 
shown  in  the  sectional  edge-view  of  the  Sun  in  Figure  II. 
In  this  manner,  most  of  the  heat  that  is  radiated  from 
its  surface  finds  its  way  into  the  force  current  and  is 
distributed  in  the  region  of  the  Sun's  equatorial  plane. 
Thus  we  see  that  the  estimates  of  the  Sun's  heat  must 
be  entirely  too  great,  when  calculations  are  based  on  the 
amount  indicated  in  different  places  on  the  Earth's  surface, 
because  the  Earth  is  always  in  or  near  the  line  of  the  Sun's 
equator. 

The  author  is  also  willing  to  admit  that  many  aerolites, 
etc.,  may  be  falling  to  the  Sun's  surface,  but  he  claims 
that  they  must  fall  to  the  surface  only  at  those  parts  where 
the  influences  are  approaching  the  northerly  or  southerly 
surfaces,  and  those  that  do  reach  the  Sun's  surface,  in  all 
probability,  remain  there,  the  same  as  they  are  known  to 
remain  on  the  Earth  after  once  reaching  it,  unless  converted 
into  gases  by  the  heat  of  the  Sun,  in  which  case  they  may 
be  driven  off  again.  It  is  neither  claimed  nor  admitted 
that  a  combustion  of  the  elements  or  influences  which  are 


68  MECHANICS   APPLIED    TO    THE    SOLAR    SYSTEM. 

drawn  to  and  sent  away  from  the  Sun  is  necessary  to  main- 
tain life  and  stimulate  growth  on  the  Earth. 

The  writer  is  also  of  the  opinion  that  but  little  of  the 
influences  which  are  drawn  toward  the  Sun,  at  the  sides 
of  the  equatorial  region,  comes  in  contact  with  the  Sun, 
but  that  they  may  be  drawn  into  the  stream  of  the  Sun's 
force  and  carried  away  many  times  before  reaching  the  Sun's 
surface. 

It  seems  that  if  this  force  were  thrown  off  before  having 
an  opportunity  to  reach  the  Sun's  surface,  it  would  be  just  as 
capable  of  carrying  the  heat  of  the  Sun  as  if  it  had  been  in 
contact  with  its  surface.  Much  of  the  heat  may  be  due  to 
the  friction  and  agitation  of  the  influences  while  they  are 
being  drawn  near  to  and  thrown  away  from  the  Sun  by  its 
centrifugal  force.  In  either  case  the  heat  seems  to  be  carried 
by  the  influences  which  are  thrown  from  the  Sun.  These 
influences  appear  to  be  drawn  to  the  Sun  at  all  times  alike. 
A  greater  or  less  quantity  of  them,  at  times  may  account  for 
the  changes  occurring  on  the  Sun's  surface. 

There  seems  to  be  no  system  by  which  the  Sun's  force 
approaches  the  Sun  that  would  imply  that  the  influences 
are  always  attracted  in  a  like  amount,  or  in  exact  or  pro- 
portional elements.  It  appears  to  attract  all  substances  to 
itself  in  the  same  way,  and  may,  at  times  and  places,  show 
by  a  slight  difference  in  its  light  a  different  composition  of 
the  elements  which  are  drawn  to  it,  as  in  the  case  of  some 
comets,  which  attract  substances  to  themselves  from  the 
space  through  which  they  are  traveling,  which  do  not,  on 
their  return,  indicate  the  same  composition  as  on  former 
visits. 

All  of  the  rotating  planets  may  be  presumed  to  throw  off 
their  heat  in  the  same  manner  as  the  Sun  and,  in  amount 
and  degree,  according  to  the  temperature  of  each  individual 
planet. 


PLANETARY    FORMATION.  69 


PLANETARY    FORMATION. 

The  two  forces,  attraction  of  gravitation  and  repulsion 
as  heretofore  represented,  appear  to  have  been  all  that  were 
in  operation  in  forming  the  Sun  and  planetary  bodies.  Al- 
though the  substance-matter  and  the  laws  of  attraction  of  grav- 
itation and  repulsion  seem  infinite  and  co-existent,  and  with- 
out beginning,  yet  the  effect  of  attraction  on  the  substance- 
matter  must  have  preceded,  in  effect,  the  repelling  action 
for  a  long  period  of  time;  for  a  substance  must  assume 
form,  then  axial  rotation,  in  order  to  develop  the  repelling 
force.  In  the  case  of  our  Sun,  the  greater  portion  of  the 
substances  of  which  it  is  composed  may  have  been  drawn 
together  before  it  acquired  an  axial  velocity  that  was  suffi- 
cient to  effectually  repel  the  substances  of  which  the  plan- 
ets are  formed,  for  we  see  that  the  several  combined  amounts 
of  the  planets  and  satellites  do  not  equal  one  five-hundredth 
part  of  the  Sun.  The  force  of  the  Sun,  like  any  other  force, 
is  capable  of  accomplishing  a  certain  amount,  and  no  more. 
That  is,  it  will  repel  substances  until  the  force  has  become 
disseminated  and  weakened,  when  the  Sun's  attraction  will 
prevent  the  substance  from  going  farther.  These  forces  of 
the  Sun  seem  to  have  located,  or  retained,  the  planetary 
substance-matter  in  their  earlier  or  original  locations,  in 
belts  or  zones  around  the  Sun,  at  distances  at  which  the 
forces  of  the  Sun  could  suspend  it,  according  to  the  grav- 
ities of  the  substances,  after  which  nuclei,  or  centers 
of  attraction,  were  formed  by  the  Sun's  agitation,  then 
axial  rotation  and  revolution  around  the  Sun,  the  larger 
body  attracting  to  itself  the  smaller  amounts,  from  a  dis- 
tance each  side  as  far  as  its  attraction  could  control  the  sub- 
stances in  opposition  to  the  Sun's  force,  beyond  which  the 
substance-matter  seeks  the  next  center  of  attraction.  These 
same  conditions  apply  to  the  formation  of  the  satellites  by 
the  attractive  and  repelling  forces  of  the  primaries. 

The  rings  of  Saturn  seem  to  furnish  a  good  illustration 
of  suspended  planetary  substance,  but  if  the  rings  are  re- 
volving with,  and  at  the  same  time  as,  the  planet,  as  some 
observers  claim,  the  agitation  of  their  substances  must  be 


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